Seminars
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Historic
An adjoint theorem for finitary functors
2024-03-19
Speaker: Lurdes Sousa (CMUC and IP Viseu)
A functor between locally presentable categories is a right adjoint iff it is accessible and preserves limits [1]. We prove that for a number of categories, called graduated, the preservation of countable limits is enough. Examples of graduated categories include sets, posets, Boolean...
Predicate liftings and lax extensions of functors
2024-03-19
Speaker: Dirk Hofmann (CIDMA, Univ. Aveiro)
Lax extensions of SET-functors to bicategories of (enriched) relations are a well-established tool in various parts of mathematics: they are fundamental in our work on "monoidal topology", but also generic notions of bisimulation for coalgebras rely on identity-preserving (=normal) lax...
The dichotomy between enriched and internal categorical structures
2024-02-27
Speaker: Rui Prezado (CMUC, Univ. Coimbra)
We revisit the dichotomy between enriched and internal categories in a base category V. By describing these objects as monads internal to certain proarrow equipments, we construct a change-of-base adjunction between the category of enriched V-categories and the category of internal...
Effective descent morphisms of Ord//X, revisited
2024-02-27
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
In this talk we will present recent results on effective descent morphisms of the lax comma category Ord//X, which improve results obtained in [2]. While in [3] effective descent morphisms of Ord, and consequently of the comma category Ord/X, were obtained making use of the category of...
A bi-equivalence for topoi with enough points
2024-01-16
Speaker: Joshua Wrigley (Univ. degli Studi dell'Insubria, Como, Italy)
Grothendieck topoi and geometric morphisms generalise topological spaces and continuous maps. Loosely speaking, a topos can be viewed as a space where the points have been endowed with the extra structure of a space of isomorphisms between points, that is, a topological...
Adjoint split extensions and 2-dimensional protomodularity
2024-01-16
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
There are a number of constructions involving categories that behave similarly to semidirect products of groups. These include Artin glueings of frames (viewed as thin categories) or toposes, and the decomposition of the category of cocommutative Hopf algebras (over a field of characteristic...
Duality for transitive partial CABAs
2024-01-09
Speaker: Rui Soares Barbosa (Iberian Nanotechnology Laboratory, Braga)
joint work with Samson Abramsky (UCL).Partial Boolean algebras (pBAs) were introduced by Kochen and Specker in their seminal work on contextuality, a key signature of non-classicality in quantum mechanics which has more recently been linked to quantum computational...
Unraveling the iterative chad
2024-01-09
Speaker: Fernando Lucatelli Nunes (CMUC & Utrecht Univ., Netherlands)
Reverse mode Automatic Differentiation (AD), a fundamental technique harnessing the chain rule to compute derivatives of functions implemented by programs, plays an integral role in addressing the challenges of efficiently computing derivatives of functions with high-dimensional domains...
On derived functors of semimodule-valued functors
2023-12-06
Speaker: Alex Patchkoria (A. Razmadze Math. Institute of Tbilisi State Univ., Georgia)
A concept of a proper projective semimodule is introduced and proper projective resolutions are used to construct derived functors of additive functors from the category of cancellative semimodules to the category of cancellative semimodules. We investigate exactness of the long sequence of...
Uniform completions via Cauchy sequences
2023-12-05
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
While the usual approach using Cauchy sequences is not powerful enough to give completions of uniform spaces in general, if handled appropriately Cauchy sequences suffice for completions of uniform locales. We describe the construction and talk about how this approach might be applied more...
Induced congruences in \(\sigma\)-frames
2023-12-05
Speaker: Raquel Bernardes (CMUC, Univ. Coimbra)
Given a \( \sigma \)-space \( X \) and its lattice of open sets \( \mathcal{O}(X) \), we will study congruences on the \( \sigma \)-frame \( \mathcal{O}(X) \) representing the subspaces of \( X \) (referred to as induced congruences). We will show that when \( X \) is a \( T_D \) \(...
More on descent theory of closure spaces and related remarks
2023-11-14
Speaker: Manuela Sobral (CMUC, Univ. Coimbra)
By a closure space we mean a set equipped with a closed under intersections set of its subsets. The purpose of this talk is to briefly recall our recent results on descent theory of closure spaces, and consider their E-versions, where E consists either of closed or of open maps, comparing...
Inverse semigroup cohomology and crossed module extensions of semilattices of groups by inverse semigroups
2023-11-14
Speaker: Mykola Khrypchenko (Univ. Porto)
We introduce the notion of a crossed module over an inverse semigroup which generalizes the notion of a module over an inverse semigroup in the sense of Lausch [1], as well as the notion of a crossed module over a group in the sense of Whitehead [4] and Maclane [3]. With any crossed \( S...
Exploring polynomial equations through Field Theory
2023-09-05
Speaker: Sophie Marques (Stellenbosch Univ., South Africa)
In this talk, we explore the intricate connections between polynomial equations, field theory, and the fascinating realm of roots of unity. Drawing on recent research advancements, we will present compelling examples that illustrate the significance of our collaborative work with Kenneth...
Topology and topoi via internal groupoids
2023-09-05
Speaker: Norihido Yamada (Univ. do Minho)
Modern game semantics grew out of the full completeness problem for linear logic and the full abstraction problem for PCF, and more recently it has been applied to the study of type systems and programming languages. My past work took a new direction by developing game semantics into a model...
A new characterization of internal groupoids
2023-05-30
Speaker: Nelson Martins-Ferreira (IP Leiria)
In this talk we will present a new characterization of internal groupoids using involutive-2-links. An involutive-2-link consists of a single morphism equipped with a pair of interlinked involutions on its domain [1]. We will see that there exists a full and faithful functor from the...
Higher-order quantitative equational theories
2023-05-30
Speaker: Renato Neves (Univ. do Minho)
Modern universal algebra frequently involves notions of equality that go beyond the standard binary setting, in which equality either holds or does not hold. In this talk we explore the idea of equality taking values from a quantale V, which covers the cases of (ultra)metric,...
Logical pluralism
2023-05-16
Speaker: Vincenzo Fano (Univ. Urbino, Italy)
The seminal book on logical pluralism written by Beall and Restall (2006) is discussed. The most relevant scholarly literature on the topic is critically presented. A more syntactical form of logical pluralism is defended. In particular, it is shown that the question of logical pluralism...
The localic groupoid classifying a geometric theory
2023-04-26
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
Famously, Joyal and Tierney proved that every Grothendieck topos can be represented as a topos of equivariant sheaves over a localic groupoid. Hence, toposes can be understood as ‘locales plus automorphisms’. However, it appears that non-experts are often unsure about exactly how...
The lax comma category Cat//X
2023-04-26
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
We will analyse the behaviour of the lax comma category Cat//X, for a given category X.
This talk is based on ongoing joint work with Fernando Lucatelli Nunes....
Polyadic sets and unnatural isomorphisms
2023-03-14
Speaker: Luca Reggio (University College London, UK)
A polyadic set over a category C is a presheaf over C satisfying an appropriate amalgamation property. Polyadic sets are a discrete variant of Joyal's polyadic spaces, which are dual to Lawvere's Boolean hyperdoctrines. I will give an overview of some basic ideas and constructions concerning...
When are there enough isomorphisms? Representing theories by groupoids of models
2023-02-23
Speaker: Joshua Wrigley (Università degli Studi dell'Insubria, Como, Italy)
For some logical theories, the data of the theory can be reconstructed from the group of automorphisms of a "special model". For example, the theory of dense linear orders can be reconstructed from the automorphism group of the rationals (considered as a dense linear order). ...
Some aspects of enriched completely distributive lattices
2023-01-24
Speaker: Dirk Hofmann (CIDMA, Univ. Aveiro)
The topics of this talk are motivated by two classic results: firstly, the fact that "Topop is a quasi-variety" proven by Barr and Pedicchio in 1995; secondly, the identification of (constructively) completely distributive lattices as the nuclear objects in the autonomous category...
Pervin spaces and Frith frames: bitopological aspects and completion
2023-01-24
Speaker: Célia Borlido (CMUC, Univ. Coimbra)
A Pervin space is a set equipped with a bounded sublattice of its powerset, while its pointfree version, called Frith frame, consists of a frame equipped with a generating bounded sublattice. It is known that the dual adjunction between topological spaces and frames extends to a dual...
On lax comma categories of ordered sets
2022-12-19
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
We will analyse the behaviour of the lax comma category Ord//X, for a complete ordered set X, namely with respect to exponentiability and descent.This talk is based on joint work with Fernando Lucatelli Nunes....
Descent for split fibrations
2022-12-19
Speaker: Fernando Lucatelli Nunes (Utrecht Univ. & CMUC)
See attached file....
The palindromization map
2022-12-13
Speaker: Dominique Perrin (Univ. Gustave-Eiffel, Paris-Est, France)
The palindromization map has been defined initially by Aldo de Luca in the context of Sturmian words. It was extended to the free group of rank 2 by Kassel and Reutenauer. We extend their construction to arbitrary alphabets. We also investigate the suffix automaton and compact suffix...
Profinite codes
2022-11-15
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
A code over the alphabet A is a nonempty subset of the free monoid over A that freely generates a free submonoid.In this talk we review some results about the topological closure of codes over A in the free profinite monoid generated by A, and present some applications of such closures to...
Taking verifiability seriously
2022-11-15
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
Interpreting open sets as verifiable properties and continuous functions as processes helps explain many aspects of topology. However, it might appear that taking this approach completely seriously sometimes leads to conclusions that contradict known results. For instance, it might seem that...
On split extensions of preordered groups
2022-10-18
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
As shown in [1], the category OrdGrp of preordered groups and monotone group homomorphisms does not satisfy the Split Short Five Lemma, although the behaviour of split extensions in OrdGrp has some interesting facets.In this talk we will study these split extensions, focusing in particular...
Jónsson categories
2022-10-18
Speaker: Diana Rodelo (CMUC & Univ. Algarve)
In this work we generalise Jónsson's theorem for congruence distributive varieties of universal algebras. The linear Mal'tsev condition extracted from the ternary Jónsson terms give rise to matrix conditions Jn, n ≥ 1. We characterise regular categories C which satisfy (the...
On categorical conditions in the semi-abelian context
2022-09-13
Speaker: James Gray (Stellenbosch University, South Africa)
The purpose of this talk is three-fold. To give an overview of categorical conditions that hold for the categories of groups and Lie algebras. To explain how a single categorical condition gives rise to all of these conditions. To explain which implications do and do not hold between these...
Algebraic geometry and tangent categories
2022-09-13
Speaker: Geoff Cruttwell (Mount Allison University, Canada)
Tangent categories, first defined by Jiri Rosicky, are a categorical structure which encompasses not only ordinary differential geometry, but also synthetic differential geometry and notions of differentiation coming from computer science.In this talk, I'll discuss how the category of affine...
When measurable spaces don't have enough points
2022-07-26
Speaker: Paolo Perrone (University of Oxford, UK)
In topology, a space is called sober if every irreducible closed subset is the closure of a unique point.One can express this concept in terms of the lower Vietoris monad, which assigns to a topological space X the space HX of its closed subsets.Given a space X, we can form a parallel pair...
The definition of pre-cohesive map in perspective
2022-07-26
Speaker: Matías Menni (Universidad Nacional de La Plata, Argentina)
Stressing topological/geometric intuition in hyperconnected geometric morphisms, we characterize the pre-cohesive ones among them. Moreover, we show that pre-cohesive maps are molecular over boolean bases....
Associativity and the co-smash product
2022-05-24
Speaker: Tim Van der Linden (Université Catholique de Louvain, Belgium)
The aim of this talk is to sketch some ideas in joint work-in-progress with Ülo Reimaa and Corentin Vienne. The original question we set out to answer was to characterise when the objects in a variety of algebras over a field K have a multiplication that is associative. What we found is...
An invitation to double categories and double fibrations
2022-05-24
Speaker: Martin Szyld (Dalhousie University, Canada)
Joint work with Geoff Cruttwell, Michael Lambert, and Dorette Pronk I will present our work on the notion of fibration for double categories [*]. I will not assume prior knowledge about double categories. Instead, I will present during the talk some basic aspects of the theory of double...
Weak adjoints and colimits in the homotopically enriched setting
2022-04-13
Speaker: John Bourke (Masaryk Univ., Brno, Czech Republic)
In category theory, one often encounters weak colimits as well as ordinary colimits. Lack and Rosicky [1] realised that can be viewed as instances of a common concept, if we work with categories enriched over a base V equipped with an appropriate class of morphisms E. Dealing with...
In search for an algebraically sound notion of a subobject in the dual of a topos
2022-04-05
Speaker: Zurab Janelidze (Stellenbosch Univ., South Africa)
A noetherian form over a category is a faithful bifibration over it, whose fibres are lattices, and which satisfies certain self-dual axioms ensuring the validity of homomorphism theorems (as stated relative to the form) from abstract algebra, such as the isomorphism theorems and homological...
Sublocales of the frame of fitted sublocales
2022-04-05
Speaker: Anna Laura Suarez (Université Côte d'Azur, France)
See the attached file. ...
Central extensions of associative algebras
2022-03-22
Speaker: George Janelidze (University of Cape Town, South Africa)
We compare descriptions of central extensions of associative R-algebras, for a commutative ring R, defined with respect to two reflections: to R-modules (equipped with the zero multiplication) and to commutative R-algebras. In both cases, the results are as expected. However, while the first...
Multiplicative lattices, groups, braces
2022-03-22
Speaker: Alberto Facchini (Università di Padova, Italy)
The multiplicative lattices we will consider are those defined in [Facchini, Finocchiaro and Janelidze, Abstractly constructed prime spectra, Algebra universalis 83(1) (published only in February 2022)]. Multiplicative lattices yield the natural setting in which several basic mathematical...
Topology for internal pre-orders: focus on complete regularity
2022-02-15
Speaker: Walter Tholen (York University, Canada)
Treating the ultrafilter monad for sets as a role model, under modest hypotheses on the two parameters involved, we consider some topological notions for T-pre-orders, internal to a category C that comes equipped with a monad T. We call them T-spaces in C, present a rudimentary theory for...
Weak factorization systems in locally presentable categories
2022-01-25
Speaker: Jiří Rosický (Masaryk Univ., Brno, Czech Republic)
We will deal with cofibrantly generated, accessible and fibrantly generated weak factorization systems in locally presentable categories. The talk is mostly based on a joint work with Sean Cox. ...
Endomorphisms of hyperbolic groups
2022-01-25
Speaker: André Carvalho (Univ. Porto, Portugal)
The Bounded Reduction Property (or Bounded Cancellation Lemma) was introduced by Cooper for automorphisms of free groups and has played an important role in the dynamical study of endomorphisms of (virtually) free groups since then.In this talk, we will present some (equivalent) geometric...
Monads on the category of metric spaces
2021-12-07
Speaker: Jirí Adámek (Technische Universität Braunschweig, Germany)
The category Met of metric spaces and nonexpanding maps is locally countably presentable in the enriched sense. It follows from the work of Kelly and Power that for countably accessible monads T on Met the category of algebras can be described as an equational category of S-algebras for a...
Lax epimorphisms and the associated factorization
2021-12-07
Speaker: Lurdes Sousa (CMUC and IP Viseu)
Lax epimorphisms (also called co-fully-faithful morphisms) are a 2-dimensional version of epimorphisms; in a 2-category A they are precisely the 1-cells f making A(f,C) fully faithful for all objects C. In this talk, several features of lax epimorphisms will be presented. We show that any...
The AIM Conjecture
2021-11-23
Speaker: Michael Kinyon (University of Denver, USA)
A long-standing open problem in loop theory has been to show that a loop with abelian inner mapping group is nilpotent of class at most 3. In this talk, I will describe the affirmative solution to this problem. No background in quasigroups or loops is needed, just some familiarity with what...
A new diagonal separation and its relations with the Hausdorff property
2021-11-23
Speaker: Igor Arrieta (PhD student, CMUC)
Let P be a property of subobjects relevant in a category C. An object X in C is P-separated if the diagonal in X × X has P; thus e.g. closedness in the category of topological spaces (resp. locales) induces the Hausdorff (resp. strong Hausdorff) axiom. In this talk we consider the...
On the ternary commutator I: Exact Mal'tsev categories
2021-10-12
Speaker: Cyrille Sandry Simeu (UCLouvain, Belgium)
Please, find the abstract attached....
An orthogonal approach to algebraic weak factorisation systems
2021-10-12
Speaker: John Bourke (Masaryk Univ., Czech Republic)
Factorisation systems (both weak and strong) are commonly defined as consisting of two classes of maps satisfying a certain orthogonality relation and a factorisation axiom. The standard definition of algebraic weak factorisation system, involving comonads and monads, is rather different. ...
Esakia duality and its connection with pointfree Pervin spaces
2021-09-14
Speaker: Anna Laura Suarez (Université Côte d'Azur, France)
Frames are complete Heyting algebras, but frame maps need not preserve the Heyting arrow. Those maps that preserve it are called open maps. Using the classical adjunction between frames and spaces, one can show that frames with open maps are dual to topological spaces with maps satisfying a...
Deciding implications of matrix properties
2021-09-14
Speaker: Michael Hoefnagel (Stellenbosch Univ., South Africa)
Matrix properties were first introduced by Z. Janelidze in 2006, as a class of exactness properties that may be represented by (extended) matrices of terms in an algebraic theory. In the simplest case, i.e., when the given algebraic theory is the algebraic theory of sets, matrix properties...
Lax factorisation systems and categories of partial maps
2021-07-20
Speaker: Leonardo Larizza (PhD student, CMUC)
Factorisation systems describe morphisms in a category by factorising them into pairs of composable morphisms. Their definition depends on an orthogonality relation between morphisms, which entails the existence of some diagonal morphisms for certain squares. In this seminar we present the...
Split extensions of bialgebras
2021-07-20
Speaker: Florence Sterck (UCLouvain, Louvain-la-Neuve)
In the category of groups, split extensions have a lot of interesting properties. One of them is the fact that the category of split extensions is equivalent to the category of group actions. Unfortunately, this does not hold in any category, for example the category of monoids does not have...
The first cohomology object in semi-abelian categories
2021-06-15
Speaker: James Gray (Stellenbosch Univ., South Africa)
We show that there is a natural notion of internal crossed homomorphism object of a split extension, defined as the representing object of a certain functor. Using these objects one can construct the first internal cohomology object of a split extension. We show that although these objects...
The reflexive completion in context
2021-06-15
Speaker: Tom Leinster (University of Edinburgh, Scotland)
For a small category A, Isbell conjugacy defines an adjunction between the functor categories [A^op, Set] and [A, Set]^op. The invariant part of this adjunction (that is, its category of fixed points) is called the reflexive completion of A.I will describe some results relating the reflexive...
Categorical aspects of the non-abelian tensor product
2021-05-25
Speaker: Tim Van der Linden (UCLouvain, Belgium)
We give an overview of joint work with Davide di Micco on an approach to the Brown-Loday non-abelian tensor product in the context of semi-abelian categories. We discuss the link with (internal) crossed squares and pairs of compatible actions, and present some examples and applications....
Congruence modular variety and algebraic crystallography
2021-05-25
Speaker: Dominique Bourn (Université du Littoral, Calais, France)
See the attached file....
Context-free word problem semigroups
2021-04-13
Speaker: Tara Brough (NOVA Univ. of Lisbon)
Please, see the attached file....
Algebraically cocomplete categories
2021-04-13
Speaker: Jiri Adámek (Technische Universität Braunschweig, Germany)
Dualizing the concept introduced by Freyd in 1990, a category is called algebraically cocomplete if every endofunctor has a terminal coalgebra. Among cocomplete categories these are just preordered classes. However, assuming the generalized continuum hypothesis (GCH), we present nice...
Minimal sets of generators
2021-03-23
Speaker: Alberto Facchini (Università di Padova, Italy)
A minimal set of generators of a right module MR over an associative ring R with identity is a subset X of M that generates M, but for any x∈ X, X∖{x} generates a proper submodule of MR. Unlike in the case of R a division ring, minimal sets of generators have little to do with...
Zariski-type spectra of localic ring-like structures
2021-03-23
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
The Zariski spectrum provides a way to associate a locale to a commutative ring. Other spectrum constructions include the Stone spectrum of a distributive lattice and the prime spectrum of an MV-algebra. In many cases the algebraic structure comes equipped with a topology which must be taken...
Colimits
2021-02-23
Speaker: Walter Tholen (York Univ., Toronto, Canada)
Extending Guitart's work of the 1970s, in this talk we eventually present the formation of the diagram category of a category and the formation of the Grothendieck category of a CAT-valued functor as adjoint 2-functors, and then establish a considerable generalization thereof. This...
Partial evaluations for monads and 2-monads
2021-02-23
Speaker: Paolo Perrone (University of Oxford, UK)
Partial evaluations are a way to encode, in terms of monads, operations which have been computed only partially. For example, the sum "1+2+3+4" can be evaluated to "10", but also partially evaluated to "3+7", or to "6+4".Such structures can be defined...
On the 3x3x3-Lemma
2021-01-19
Speaker: Tim Van der Linden (UCLouvain, Belgium)
The idea of a short exact sequence of short exact sequences naturally leads to the 3x3-Lemma. What happens when this process is repeated? The aim of this talk is to explain the connection between the concept of a 3-fold extension, short exact sequences of 3x3-diagrams, and a congruence...
Abstract and concrete spectral spaces
2021-01-19
Speaker: George Janelidze (Univ. Cape Town, South Africa)
In this joint work with Alberto Facchini and Carmelo Antonio Finocchiaro we begin with a complete lattice L equipped with a binary multiplication such that the product of any two elements is less or equal to their meet. As suggested by the so-called "Abstract ideal theory" we...
A new approach to S-protomodular categories
2021-01-05
Speaker: Tamar Janelidze-Gray (Univ. Cape Town, South Africa)
We propose a new approach to S-protomodular categories in the sense of D. Bourn, N. Martins-Ferreira, A. Montoli, and M. Sobral. Instead of points (=split epimorphisms) it uses generalized points, which we define as composable pairs of morphisms whose composites are pullback stable regular...
Relaxed actions of monoids: Towards a new cohomology theory
2021-01-05
Speaker: Peter Faul (University of Cambridge, UK)
Artin glueings between frames have much in common with semidirect products of groups. If H and N are groups (frames) then the process of constructing semidirect products (Artin glueings) provides a means of finding all objects in which N embeds as a normal (closed) subobject and H embeds as...
Characterizations of normality given by \(C\)-, \(C^*\)- and \(z\)-embedded sublocales
2020-12-02
Speaker: Ana Belén Avilez (PhD student, CMUC)
Please, see the attached file....
Sublocales as parts
2020-12-02
Speaker: Imanol Mozo Carollo (Univ. of the Basque Country, Bilbao, Spain)
Please, find the attached file....
Characterization of coextensive varieties of universal algebras
2020-11-10
Speaker: David Neal Broodryk (University of Cape Town, South Africa)
A coextensive category can be defined as a category C with finite products such that for each pair X,Y of objects in C, the canonical functor ×:X/C×Y/C→(X×Y)/C is an equivalence. This is the dual of an extensive category, a term that was first used by W. F. Lawvere and...
Pretorsion theories and internal preorders
2020-11-10
Speaker: Marino Gran (UCLouvain, Belgium)
Please, find the attached file....
The theory of exactness properties: recent developments and work in progress
2020-10-13
Speaker: Zurab Janelidze (Stellenbosch University, South Africa)
By the "theory of exactness properties" we mean a subject that is in similar relation to the theories of semi-abelian categories, abelian categories, etc., as universal algebra is to group theory, module theory, etc. These classes of categories (semi-abelian, abelian, etc.) are...
Variations on distributive laws
2020-10-13
Speaker: Nicola Gambino (University of Leeds, UK)
The notion of a distributive law between monads goes back to fundamental work of Jon Beck from the late ‘60s. Just as a monad describes a kind of algebraic structure, a distributive law between two monads describes how the algebraic structure for one monad distributes over the...
The Karoubi envelope of the mirage of a subshift
2020-09-15
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
Free profinite semigroups are completions of free semigroups, and for that reason their elements are frequently called pseudowords. Around 2003, Almeida introduced a fruitful connection between symbolic dynamical systems (also known as subshifts) and free profinite semigroups. Following...
The polycyclic inverse monoids and the Thompson groups revisited
2020-09-15
Speaker: Mark Lawson (Heriot-Watt University, UK)
Please, see the attached file....
Discrete covers of locales
2020-07-14
Speaker: Igor Arrieta Torres (PhD Student, CMUC)
See attached file....
Some fibrational properties of normal monomorphisms
2020-07-14
Speaker: Giuseppe Metere (Universitá degli Studi di Palermo, Italy)
Several classes of monomorphisms have been introduced in general algebraic contexts. For some of them, there is a purely categorical description that makes it possible a formal study of their structure. In my talk, after a quick recap of such notions, I will focus on the normal subobjects in...
Tensors of KZ-algebras
2020-06-30
Speaker: Marcelo Fiore (University of Cambridge, UK)
We investigate tensors of pseudo-algebras for KZ (aka lax idempotent) 2-monads. Our leading example is the tensor product of (unsorted) algebraic theories. This will be used throughout the talk to motivate and present the abstract theory.We shall consider tensors both in the sense of...
Characterizations of lax orthogonal factorization systems
2020-06-30
Speaker: Charles Walker (Masaryk University, Czech Republic)
See attached file....
Intrinsic Schreier split extensions and intrinsic Schreier special objects
2020-06-02
Speaker: Andrea Montoli (Univ. degli Studi di Milano, Italy)
We explore, in the context of regular unital categories with comonadic projective covers, intrinsic notions of Schreier split epimorphisms and Schreier special objects. These intrinsic notions allow, on one hand, to understand categorically the properties of Schreier split extensions of...
Double categories of open dynamical systems
2020-06-02
Speaker: David Jaz Myers (Johns Hopkins University, USA)
A dynamical system consists of a notion of how things may be, and a notion of how things may change, given how they are. There are many sorts of dynamical systems --- discrete, continuous, probabilistic, non-deterministic --- and the dynamics often depend on parameters which themselves may...
From preordered groups to quantale-enriched groups
2020-05-05
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
Based on the study of preordered groups of [1], we introduce and study V-groups and their homomorphisms, for a commutative and unital quantale V.(This talk is based on joint work with Andrea Montoli [2].) References:[1] M.M. Clementino, N. Martins-Ferreira, A. Montoli, On the...
Actions of preordered monoids and their associated extensions
2020-05-05
Speaker: Nelson Martins-Ferreira (IP Leiria, CDRSP)
The category of preordered monoids can be seen either as a category of internal preorders in monoids or as the category of internal monoids in preorders. In this talk, we start by analysing differences and similarities between preordered groups and preordered monoids. In particular, we study...
Revisiting the relation between subspaces and sublocales
2020-02-18
Speaker: Anna Laura Suarez (Univ. Birmingham, UK)
One of the main features distinguishing pointfree topology from classical point-set one is that in the pointfree setting a space (i.e. a locale) may have abstract subspaces (sublocales) which do not have any point-set analogue. The lattice of sublocales of a locale will not in general be a...
Enriched Priestley spaces
2020-02-18
Speaker: Dirk Hofmann (Univ. Aveiro)
See attached file....
On difunctionality of class relations
2020-01-31
Speaker: Diana Rodelo (CMUC and Univ. Algarve)
See attached file....
Categorical aspects of congruence distributivity
2020-01-31
Speaker: Idriss Tchoffo Nguefeu (UCLouvain, Belgium)
We give new characterisations of regular Mal'tsev categories with distributive lattice of equivalence relations through variations of the so-called Triangular Lemma and Trapezoid Lemma in universal algebra. We then give new characterisations of equivalence distributive Goursat categories...
Finitely presentable algebras for finitary monads
2019-12-17
Speaker: Lurdes Sousa (CMUC and IP Viseu)
A variety of algebras is nothing else than the category of algebras of a finitary monad on Set, and, in this case, an algebra A is finitely presentable if it can be presented by a finite set of generators and a finite set of equations. We generalize this to finitary regular monads on...
Stone pseudovarieties
2019-11-19
Speaker: Jorge Almeida (CMUP, Univ. Porto)
Profinite algebras have been extensively considered in the literature, particularly in the realms of groups and semigroups. They are the residually finite topological algebras over Stone spaces. In this talk, we consider classes of Stone topological algebras of a fixed signature that are...
Split extensions of monoids and Hopf algebras
2019-11-19
Speaker: Florence Sterck (Université catholique de Louvain, Belgium)
In the category of groups, split extensions have a lot of interesting properties. One of them is the fact that the category of split extensions is equivalent to the category of group actions.Unfortunately, this property doesn't hold in the category of monoids. Nevertheless, it was proved in...
Functorial semantics and descent II
2019-10-15
Speaker: Fernando Lucatelli Nunes (CMUC, Univ. Coimbra)
Restricting our attention to the 2-category of categories, the main result of [1] gives in particular a natural factorization of functors via descent. Moreover, under suitable hypothesis, this factorization is shown to coincide with the semantic factorization of the functor. This gives as a...
Injectives via actions or: How I learned to stop worrying and love quantales
2019-10-15
Speaker: Eros Martinelli (CIDMA, Univ. Aveiro)
In this talk, motivated by a classical result that relates injectives V-categories with injectives (= complete) ordered sets with an action, we prove a similar result for (L,V)-categories where L is the list monad....
Colimit-dense subcategories
2019-04-23
Speaker: Jiří Adámek (Tech. Univ. Braunschweig, Germany)
A small full subcategory K' of a category K is called dense (or colimit-dense) if every object X of K is a colimit of some diagram in K' (or is the canonical colimit of all maps from objects of K' to X, resp.). The existence of a colimit-dense subcategory is an important property, e.g., the...
Crossed semimodules of cancellative conjugation monoids
2019-04-23
Speaker: Nelson Martins Ferreira (CDRSP, ESTG, IP Leiria)
This talk is based on the work [1] where we show that the category of cancellative conjugation semigroups is weakly Mal'tsev and give a characterization of all admissible diagrams there.In the category of cancellative conjugation monoids we describe, for Schreier split epimorphisms with...
Decidability of first-order theories
2019-03-26
Speaker: Cristina Sernadas (CMAFcIO, Univ. Lisboa)
Some results and reduction techniques for proving decidability of mathematical theories and completeness of logics are presented. The crucial role of the theory of real closed ordered fields is explained. Selected illustrations from Euclidean Geometry to Quantum Logic are discussed....
On the classification of Schreier extensions of monoids with non-abelian kernel
2019-02-12
Speaker: Andrea Montoli (Univ. degli Studi di Milano, Italy)
We will show that any regular right Schreier extension of a monoid M by a monid A induces an abstract kernel, i.e. a monoid homomorphism from M to the factor monoid End(A)/Inn(A). If an abstract kernel factors through Epi(A)/Inn(A), then we associate to it an obstruction, which is an element...
Order-enriched solid functors
2019-02-12
Speaker: Lurdes Sousa (CMUC and IP Viseu)
Order-enriched solid functors enjoy many of the properties of their counterparts, including the detection of weighted colimits. We study two slightly different notions of order-enriched solidity and present several examples, which include functors of general varieties of ordered algebras and...
From quantum to quantales and beyond
2019-01-22
Speaker: Pedro Resende (CAMGSD, Univ. Lisboa)
[The following abstract may also be found in the PDF file that is attached to this announcement] The axioms of quantum mechanics laid out by von Neumann involved Hilbert spaces and operators on them, and it soon became apparent that the properties of collections of operators are...
Axiom \(T_D\) and the Simmons sublocale theorem
2019-01-22
Speaker: Jorge Picado (CMUC, Univ. Coimbra)
A topological space \( X \), more precisely its associated frame \( \Omega(X) \) of open sets, has typically more sublocales than subspaces. We will analyze some of Simmons (1980) and Niefield and Rosenthal (1987) results concerning sublocales induced by subspaces.
The first result...
Functorial semantics and descent
2018-12-18
Speaker: Fernando Lucatelli Nunes (CMUC, Univ. Coimbra)
In [1], given a 2-category A satisfying suitable hypothesis, we give the semantic factorization via descent. This specializes to a new connection between monadicity and descent theory, which can be seen as a counterpart account to the celebrated Bénabou-Roubaud Theorem [2]. It also...
Compactly generated (T,V)-spaces
2018-12-18
Speaker: Willian Ribeiro (PhD Student, CMUC)
First studied by Hurewicz, compactly generated spaces arise as a convenient category for homotopy theory and algebraic topology [1]. The full subcategory of Top (the category of topological spaces and continuous functions) formed by the latter spaces is well-known to have nice properties: it...
On the linear nature of pseudowords
2018-11-28
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
In this talk we see how the pseudowords in a finitely generated free profinite aperiodic semigroup are faithfully represented by labeled linear orders induced by factorizations of the pseudowords.This is joint work with Jorge Almeida, José Carlos Costa and Marc Zeitoun. ...
Limit groups and their profinite completion
2018-10-16
Speaker: Theo A. D. Zapata (Univ. de Brasília, Brazil)
In the last decades limit groups have been attracting the attention of many mathematicians, specially because they played a fundamental role in the recent solution of the outstanding Tarski problem on free groups. Two simple group-theoretical reasons for so much attention are the following:...
A categorical model for the Hopf fibration
2018-10-16
Speaker: Björn Gohla (GFM, Univ. Lisboa)
We give a description up to homeomorphism of S3 and S2 as classifying spaces of small categories, such that the Hopf map S3 --> S2 is the realization of a functor....
An Eilenberg-like Theorem beyond regular languages
2018-07-06
Speaker: Célia Borlido (Univ. Nice Sophia-Antipolis, France)
(See the attachment for the pdf version of the abstract). Finite and profinite monoids have proved to be a powerful tool in the study of regular languages. On the one hand, Eilenberg's correspondence, establishing a bijection between certain classes of regular languages (so-called...
Galois theory of graphs
2018-06-29
Speaker: George Janelidze (Univ. Cape Town, South Africa)
This talk is about graphs in the sense of graph theory (not in the sense used in category theory). It will be shown that their Galois theory is not very different from other set-valued combinatorial Galois theories considered before, in spite of what it seems, due to non-existence of various...
On generating cartesian closed subcategories of (T,V)-Cat
2018-06-29
Speaker: Willian Ribeiro (PhD Student, CMUC)
Generalizing the work of [1], we present the process of generating cartesian closed subcategories of (T,V)-Cat. From a fixed class C of objects, we form a new (reflective) subcategory whose objects are shown to be colimits of objects in C. For instance taking for C the class of compact...
Towards semi left exactness and Janelidze-Galois within the lax idempotent context
2018-06-29
Speaker: Fernando Lucatelli Nunes (CMUC)
This is a joint work with Maria Manuel Clementino. Our aim is to understand the analogues of semi-left exactness and the analogues of the basic ideas of Janelidze-Galois within the lax idempotent context. As it is usual, there are more than one possible approach to do so. Our first...
On the profinite topology on solvable groups
2018-05-23
Speaker: Khadijeh Alibabaei (CMUP, Univ. Porto)
We show that the wreath product of a finitely generated abelian group with a polycyclic group is a LERF group. This theorem yields as a corollary that the finitely generated free metabelian group is LERF, a result due to Coulbois.We also show that the finitely generated free solvable group...
The nine lemma in the S-Mal'tsev and in the S-protomodular settings
2018-04-17
Speaker: Andrea Montoli (Univ. degli Studi di Milano, Italy)
We investigate what is remaining of the nine lemma and of the denormalized nine lemma, respectively valid in a pointed protomodular and in a Mal'tsev category, in the context of partial protomodular and partial Mal'tsev categories, relatively to a class S of points. The results apply, among...
On homology monoids of simplicial abelian monoids
2018-04-17
Speaker: Alex Patchkoria (A. Razmadze Math. Institute of Tbilisi State Univ., Georgia)
The homology semimodules Hn(S) of a presimplicial semimodule S introduced in our earlier paper, are studied in the case where S is a simplicial abelian monoid. In particular, it is shown that if a simplicial abelian monoid A satisfies the Kan condition and the monoid of path components...
Rewriting systems and commutativity of diagrams
2018-03-20
Speaker: Ivan Yudin (CMUC, Univ. Coimbra)
It is a common situation that given a set of commutative diagrams one needs to establish commutativity of another set of diagrams. The naive approach to the problem is to partition each diagram into smaller diagrams, so that each subdiagram is in the given set of commutative diagrams.In the...
Topological groups have representable internal actions
2018-03-20
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
The actions of a group B on a group X correspond bijectively to the group homomorphisms from B to the group of automorphisms of X. This can be stated using representability of the functor 'actions on X' (see [2, 3]).In this talk we show the corresponding result for topological groups: The...
The intricacies of algebraic power series
2018-02-07
Speaker: Herwig Hauser (Univ. of Vienna, Austria)
A formal power series h(x) = sum a_n x^n is called algebraic if it satisfies a polynomial equation with coefficients in K[x]. Typical examples are rational series like (1+x)^(-1) or roots of polynomials like sqrt(1+x). In characteristic 0, it is an open problem to characterize the...
The category of Brouwer operations: a basis for an understanding of choice sequences
2018-01-23
Speaker: Martin Hyland (Univ. of Cambridge, UK)
Intuitionism as first proposed by the Dutch mathematician L. E. J. Brouwer involved not simply the well-known refusal of the law of the excluded middle but a notion, that of free choice sequence which is prima facie incompatible with classical mathematics. The theory of choice sequences uses...
2-Representations of dihedral and trihedral Soergel bimodules
2018-01-23
Speaker: Marco Mackaay (Univ. Algarve)
2-Representation theory of monoidal categories is the categorical analogue of representation theory of algebras. In my talk, I will discuss the 2-representation theory of (sub)-quotients of the monoidal categories of Soergel bimodules of affine type A1 and A2, which are closely related to...
Right-angled Artin groups: commensurability classification and subgroup intersection problem
2017-12-13
Speaker: Alexander Zakharov (CMUP, Univ. Porto)
The class of right-angled Artin groups (RAAGs) is a prominent class of groups which is widely studied in different branches of mathematics and computer science. Two groups are called commensurable if they have isomorphic subgroups of finite index. In the first part of the talk I will present...
Continuous weak selections on compact-like spaces
2017-11-21
Speaker: Tsugunori Nogura (Ehime Univ., Japan)
See attached file....
Inverse monoids and immersions of cell complexes
2017-10-17
Speaker: Nora Szakács (CMUP, Univ. Porto)
In the talk, we study immersions between cell complexes using inverse monoids. By an immersion f : D -> C between cell complexes, we mean a continous map which is a local homeomorphism onto its image, and we further suppose that commutes with the characteristic maps of the cell complexes....
Joins of closed sublocales, coframes of sublocales, and frames of sublocales
2017-09-12
Speaker: Aleš Pultr (Charles Univ., Prague, Czech Republic)
Topics to be covered: 1. The frame Sc(L) of joins of closed sublocales of a locale L; motivation (scatteredness). 2. The relation of Sc(L) to the coframe of sublocales S(L). 3. Sc(L) as a "discrete cover" of L, modelling discontinuity. 4. Comparing Sc(L) with the frame of...
Towards a pseudoequational proof theory
2017-07-13
Speaker: Jorge Almeida (CMUP, Univ. Porto)
A new scheme for proving pseudoidentities from a given set Σ of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when Σ defines a locally finite variety, a pseudovariety of groups or, more generally, of completely simple...
Corecursive algebras
2017-04-26
Speaker: Jiří Adámek (Tech. Univ. Braunschweig, Germany)
There are various models of algebras in which certain recursive equations are uniquely solvable. A simple one was introduced by Capretta, Uustalu and Vene: given an endofunctor H, recursive equations are formalized as coalgebras for H. An algebra for H is called corecursive if every...
Graph complexes and configuration spaces of points
2017-04-19
Speaker: Ricardo Campos (ETH Zürich, Switzerland)
Given a manifold M, one can study the configuration space of n points on the manifold, which is the subspace of M^n in which two points cannot be in the same position. The study of these spaces from a homotopical perspective is of interest in very distinct areas such as algebraic topology or...
An introduction to \(L_\infty\) algebras and \(L_\infty\) algebroids
2017-04-19
Speaker: Raquel Caseiro (CMUC/Univ. Coimbra)
\( L_\infty \) algebras are natural generalizations of Lie algebras from a homotopy theoretical point of view. The original definition dates back to 1992 by J. Stasheff and T. Lada and the idea is to weaken the condition imposing that the Lie bracket satisfies the Jacobi identity. Instead...
Magnitude homology
2017-04-11
Speaker: Tom Leinster (Univ. of Edinburgh, UK)
Magnitude homology is a homology theory of enriched categories, proposed by Michael Shulman late last year. For ordinary categories, it is the usualhomology of a category (or equivalently, of its classifying space). But for metric spaces, regarded as enriched categories à la...
Resolvability of topological spaces
2017-03-31
Speaker: István Juhász (Alfréd Renyi Inst. of Mathematics, Budapest, Hungary)
A topological space X is called λ-resolvable, where λ is a (finite or infinite) cardinal, if X contains λ many pairwise disjoint dense subsets. X is maximally resolvable if it is ∆(X)-resolvable, where ∆(X) = min{|G| : G open, G =/= ∅} .The...
On some categorical-algebraic conditions in S-protomodular categories
2017-03-21
Speaker: Andrea Montoli (Università degli Studi di Milano, Italy)
We study, in the context of S-protomodular categories, relative versions of some categorical-algebraic conditions already considered for semi-abelian categories, like the algebraic coherence and the local algebraic cartesian closedness. The goal is to obtain a hierarchy between...
Interesting algebras between Kleisli and Eilenberg-Moore
2017-03-21
Speaker: Lurdes Sousa (CMUC, IP Viseu)
We investigate important categories lying strictly between the Kleisli category and the Eilenberg-Moore category, for a Kock-Zöberlein monad on an order-enriched category. The situation is dramatically different from the particular case of idempotent monads, for which there are no...
Dual enrichment and Isbell Duality
2017-01-30
Speaker: Martin Hyland (Univ. of Cambridge, UK)
The category of presheaves on a given small category is enriched in the category of presheaves on its opposite. This piece of Category Theory folklore is under appreciated perhaps because it is not clear what to do with it. I shall discuss versions of this phenomenon and how it looks from...
Sign patterns of coefficients of power series associated with the spectra of positive matrices
2017-01-30
Speaker: Thomas Laffey (Univ. College Dublin, Ireland)
See attached pdf file....
How to centralize and normalize quandle extensions
2016-12-13
Speaker: Mathieu Duckerts-Antoine (CMUC)
During this talk, we will study different classes of quandle homomorphisms defined with respect to a fundamental reflection of the category of quandles into its full subcategory of trivial quandles. I will recall the notion of a central extension and of a normal extension coming from...
Monoidal categorical Galois theory
2016-11-15
Speaker: Dimitri Chikhladze (CMUC, Univ. Coimbra)
In this talk I will explain a generalization of the categorical Galois theory of Janelidze to a context of monoidal category theory, and its relationship with the work of Deligne on Tannakian categories....
Equidivisible pseudovarieties of semigroups
2016-11-15
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
A semigroup is said to be equidivisible if distinct factorizations of an element have always a common refinement. Groups and free semigroups are examples of equidivisible semigroups.We give a complete characterization of pseudovarieties of semigroups whose finitely generated relatively free...
The deficiency of categories
2016-10-25
Speaker: Fernando Lucatelli Nunes (CMUC)
The study of the deficiency of a category arises from the problem of understanding what is a presentation of a category with the least number of equations and, therefore, avoiding redundancy.I have been studying deficiency within the context of descent and lifting of biadjoints (within the...
Semigroup of endomorphisms of a vector space
2016-06-27
Speaker: A. R. Rajan (Univ. Kerala, India)
The semigroup of endomorphisms of a finite dimensional vector space is an extensively studied object in semigroup theory. Often it is identified with the semigroup M_n(K) of n × n matrices over a field K. As a ring M_n(K) is a basic ring used in structure theory of rings. Hence the...
Cross-connections of balanced categories
2016-06-27
Speaker:
P. G. Romeo (Cochin Univ., India)
In this talk I will explain what a balanced category is and show that the ideal categories of a concordant semigroup are balanced categories. I will also mention about the cross-connection of such categories.An extended abstract of the talk is attached herewith....
The LEGO of localic maps
2016-05-17
Speaker: Jorge Picado (CMUC, Univ. Coimbra)
Assembling a localic map f : L → M from localic maps fi : Si → M, i ∈ J, defined on closed resp. open sublocales (J finite in the closed case) follows the same rules as in the classical case. The corresponding classical facts immediately follow from the behavior of preimages...
Reflectivity and its logics
2016-05-17
Speaker: Lurdes Sousa (CMUC, IP Viseu)
In previous joint work with Jirí Adámek and Manuela Sobral we presented a logic for finitary epimorphisms which can be seen as an extension of Birkhoff's equational logic. In subsequent papers joint with Jirí Adámek and Michel Hébert, we...
An overview over conjugacy in semigroups
2016-04-13
Speaker: António Malheiro (Univ. Nova de Lisboa, CMA)
When generalizing a concept, it is sometimes tempting to think that there should be one correct, or even preferred, generalization. Since semigroup theory is a vast subject, intersecting many areas of pure and applied mathematics, it is probably not reasonable to expect a one-size-fits-all...
Higher centrality via degenerate simplices
2016-03-22
Speaker: Tim Van der Linden (Univ. Catholique de Louvain, Belgium)
When, in a semi-abelian category, a truncated simplicial object is considered as a higher extension, the commutators involved in the centrality condition for this extension may be expressed in terms of degenerate simplices. The aim of my talk is to explain some of the simplicial-geometrical...
The Beck-Chevalley property for Goursat categories
2016-03-22
Speaker: Diana Rodelo (CMUC, Univ. Algarve)
We characterise regular Goursat categories through a specific stability property of regular epimorphisms with respect to pullbacks. Under the assumption of the existence of some pushouts this property can be also expressed as a restricted Beck-Chevalley condition, with respect to the...
On a version of homological algebra in the category of semimodules and its applications
2016-02-16
Speaker: Alex Patchkoria (A. Razmadze Math. Institute of Tbilisi State Univ., Georgia)
We develop a version of homological algebra for semimodules which enables us to: (1) introduce new cohomology monoids of an arbitrary monoid M with coefficients in semimodules over M as more computable alternatives to the old ones, (2) construct singular ...
The action of a 2-group on a category and its application in higher gauge theory
2016-02-01
Speaker: Roger Picken (IST, Univ. Lisboa)
The fundamental notion of symmetry can be expressed as the action of a group on a set, or more generally in terms of a transformation groupoid. In this talk I will show how a group action on a set may be generalized to a 2-group action on a category C, and how such an action gives rise to a...
Howson's property for semidirect products of semilattices by groups
2016-02-01
Speaker: Filipa Soares de Almeida (CEMAT and ISEL, Lisboa)
Howson's Theorem (1954), a classical result in group theory, established that the intersection of two finitely generated subgroups of a free group always yields a finitely generated subgroup. Jones and Trotter (1989) showed that is not the case for any free inverse semigroup with more than...
The Universal Generalization Problem. Euclid's mathematical solutions and contemporary formal accounts
2016-01-18
Speaker:
Pierluigi Graziani (University of Chieti-Pescara - Italy)
The goal of my talk is to analyze different contemporary foundations of Euclid's Geometry [1], compare them with each other and with the philological studies of ancient texts. In particular, I will analyze how these foundational studies fare with respect to the Universal Generalization...
The poset of proper divisibility
2016-01-18
Speaker: Antonio Macchia (CMUC)
Inspired by the definition of the Buchberger graph of a monomial ideal, we study proper divisibility of monomials as a partial order in N^n, from a combinatorial and topological point of view. From this order relation we obtain a new family of posets, that we call posets of proper...
Homotopy theory of 2-categories
2015-12-15
Speaker: Benjamín Alarcón Heredia (CMA, FCT-UNL)
The category of small categories has a Thomason model structure making its homotopy category equivalent to the classical homotopy category of topological spaces. The same is true for small 2-categories, so we can think of small 2-categories as spaces. In this talk I will present the...
The rank of variants of nilpotent pseudovarieties
2015-12-15
Speaker:
M. Hossein Shahzamanian C. (CMUP, Univ. Porto)
In this talk, we investigate the rank of classes defined by several of the variants of nilpotent semigroups in the sense of Mal'cev. For several of them, we even give finite basis of pseudoidentities. We show that the pseudovariety $\mathsf{NT}$ has infinite rank and, therefore, it is...
What is Nelson's admissibility condition?
2015-11-10
Speaker: Tim Van der Linden (Université Catholique de Louvain, Belgium)
In his Ph.D.thesis [3], Nelson Martins-Ferreira introduced a technical condition (for a certain type of diagram in a category) which he called admissibility. His first aim was to efficiently describe internal categorical structures, but the flexibility of the condition allowed him to use it...
A characterization of central extensions in the variety of quandles
2015-11-10
Speaker: Andrea Montoli (CMUC, Univ. Coimbra)
The category of symmetric quandles is a Mal'tsev variety whose subvariety of abelian symmetric quandles is the category of abelian algebras. We give an algebraic description of the quandle extensions that are central for the adjunction between the variety of quandles and its subvariety of...
Biadjoint triangles, descent and coherence
2015-10-13
Speaker: Fernando Lucatelli Nunes (CMUC, Univ. Coimbra)
Firstly, we talk about the general result of coherence due to Power-Kelly-Blackwell and Lack. Then, we show how this motivates the study of a 2-dimensional version of Eduardo Dubuc's adjoint triangle theorem.At last, we show what the proofs of the (bi)adjoint triangle theorems have to do...
Functional representations of monads in duality theory
2015-10-13
Speaker: Pedro Nora (Univ. Aveiro)
It is well known that Stone's classical duality theorems can be generalised to categories of spaces and continuous relations. For example, Halmos's duality theorem affirms that the category of Stone spaces and Boolean relations (relations which are continuous in an appropriate sense) is...
The meet formula for pseudocomplement and an aspect of the coframe of sublocales
2015-09-09
Speaker: Aleš Pultr (Charles Univ., Prague, Czech Republic)
A frame is a complete Heyting algebra; in particular it is pseudocomplemented and we have the formula a^* = \bigvee{x : x \wedge a = 0}. Dually, in a coframe we have the formula for the supplement a^# = \bigwedge{x : x v a = 1}. (#) Somewhat surprisingly, under suitable (and very...
Supernilpotent algebras are non-dualizable
2015-07-07
Speaker: Wolfram Bentz (CEMAT-FCUL, Univ. de Lisboa)
Natural dualities, such as Stone duality, are useful because they allow one to translate algebraic questions into the potentially simpler and usually more intuitive setting of a topological structure. If these dualities exist for particular classes of algebras, then they can be obtained in a...
The Karoubi envelope and the Schützenberger category of a semigroup.
2015-07-07
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
The Karoubi envelope plays a fundamental role in Tilson's Delay theorem, an important result in the theory of pseudovarieties of semigroups. It is also known that two semigroups with local units are Morita equivalent if and only if they have equivalent Karoubi envelops.We introduce a new...
Kan-injectivity of locales and spaces
2015-05-19
Speaker: Lurdes Sousa (IP Viseu and CMUC)
Two well-known important facts are the characterization of the continuous lattices as the spaces injective with respect to embeddings in the category Top0 of T0 topological spaces (D. Scott, 1972), and the characterization of the stably locally compact locales as the locales injective with...
What is an ideal a zero-class of?
2015-05-19
Speaker: Andrea Montoli (CMUC)
We characterize, in pointed regular categories, the ideals as the zero-classes of surjective relations. Moreover, we study a variation of the ''Smith is Huq'' condition: two surjective left split relations commute as soon as their zero-classes commute.Joint work with Nelson Martins-Ferreira,...
Monóides de Ehresmann
2015-04-15
Speaker: Gracinda M.S. Gomes (DM-FCUL e CEMAT-FCUL, Univ. Lisboa)
Na teoria dos monóides inversos a classe dos próprios, ou E-unitários, tem um papel crucial, já que todo o monóide inverso tem uma cobertura própria (que separa idempotentes), um monóide inverso próprio ...
Borel-Schur algebras of finite representation type
2015-04-15
Speaker: Ivan Yudin (CMUC)
In my talk I will explain what is the representation type of a finite dimensional algebra. Then I will describe the Borel-Schur algebras of finite type. This is a joint work with K. Erdmann and A.P. Santana....
Peiffer product and Peiffer commutator for internal pre-crossed modules
2015-03-24
Speaker: Alan S. Cigoli (Università degli Studi di Milano, Italy)
In this work we introduce the notions of Peiffer product and Peiffer commutator of internal pre-crossed modules over a fixed object B, extending the corresponding classical notions to any semi-abelian category. We prove that, under mild additional assumptions on the category, crossed modules...
The localic group of the unit circle
2015-03-24
Speaker:
Imanol Mozo Carollo (UPV/EHU, Bilbao, Spain)
The category of locales, which is the object of study of pointfree topology, has an algebraic dual, the category of frames. This fact was used by Joyal in order to introduce the frame of reals as a pointfree counterpart of the real line [3]. Further, this lead to a fruitful study of the...
Plactic, hypoplactic, and Sylvester monoids, and other homogeneous monoids
2015-02-25
Speaker: Alan Cain (CMA, Univ. Nova de Lisboa)
In recent work with Gray and Malheiro, I proved that finite-rank plactic monoids (in which Young tableaux form a cross-section) admit finite convergent presentations and are biautomatic. This seminar will survey three themes arising from this work: (1) Using similar techniques with rather...
From ordered to metric compact Hausdorff spaces
2015-01-13
Speaker: Dirk Hofmann (Univ. Aveiro)
The aim of this talk is to lift the well-known equivalence between ordered compact Hausdorff spaces and stably compact spaces to the metric world, together with several constructions involving these types of spaces....
On the "Smith is Huq" condition in S-protomodular categories
2015-01-13
Speaker: Andrea Montoli (CMUC)
We study the so-called "Smith is Huq" condition in the context of S-protomodular categories: two S-equivalence relations centralise each other if and only if their normalisations commute. We prove that this condition is satisfied by every category of monoids with operations...
Monoid theoretic approach to bicategorical structures
2014-12-09
Speaker: Dimitri Chikhladze (CMUC, Univ. Coimbra)
We develop a lax version of the formal theory of monads, and consider its connection with the bicategorical structures and the theory of generalized operads. ...
Quasi-F frames
2014-11-25
Speaker: Mack Matlabyana (Univ. Limpopo, South Africa)
A completely regular frame L is said to be quasi-F if for every dense c ∈ CozL, the open quotient L →↓a is a C*-quotient map.Quasi-F frames generalize almost-P frames and F'-frames. The intention of the talk is to give several characterizations of these frames....
On topological semi-abelian algebras: split extensions and their classifiers
2014-11-25
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
Actions of a group B on a group X correspond bijectively to split extensions of B with kernel X, or to semidirect products of X and B, or to group homomorphisms from B to the group Aut(X) of automorphisms of X. This last property of Aut(X) is usually identified as representability of...
Involutive double categories
2014-10-28
Speaker: Rachel A.D. Martins (IST/UL)
A double category has an equivalent description as a double partial monoid, that is, a set equipped with two partial monoid structures such that all structure maps are partial monoid homomorphisms. Double categories can have an interesting and natural involutive structure, which we ...
Some remarks on descent for Priestley spaces
2014-10-28
Speaker: Manuela Sobral (CMUC, Univ. Coimbra)
In this talk the problem of characterizing effective descent morphisms for Priestley spaces is recalled and solved in two veryspecial cases: for maps with finite codomain and for maps that are open and order-open, or, equivalently, open and order-closed....
Fundamental group functors and higher Hopf formulae
2014-09-30
Speaker: Mathieu Duckerts-Antoine (CMUC)
In 1988, R. Brown and G. J. Ellis gave Hopf formulae for the integral homology of a group using topological methods. G. Janelidze first recognized that these descriptions are deeply connected with the categorical Galois-theoretic notion of covering morphism. Using this perspective, T....
Lax algebras as spaces
2014-09-30
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
Following [1], in this talk we look at lax algebras as spaces, exploring their topological properties like compactness, Hausdorff separation, regularity, normality and extremal disconnectedness. [1] M.M. Clementino, E. Colebunders, W. Tholen, Lax algebras as spaces, in: Monoidal...
The pointfree representation of a truncated archimedean l-group
2014-09-11
Speaker: Richard N. Ball (Univ. Denver, USA)
In this talk we develop the analog for truncated archimedean lattice-ordered groups, hereafter referred to as truncs, of Madden's pointfree representation for W, the category of archimedean l- groups with designated weak order unit. In the first part of the talk we will motivate the notion...
Pointfree pointwise suprema in archimedean l-groups
2014-09-10
Speaker: Richard N. Ball (Univ. Denver, USA)
We generalize the concept of the pointwise supremum of real-valued functions to the pointfree setting. The concept itself admits a direct and intuitive formulation which makes no mention of points. But our aim here is to investigate pointwise suprema of subsets of RL, the family of...
Kan-injectivity in Top0 and Kan-projectivity in Frm
2014-07-10
Speaker: Margarida Carvalho (ISCAC)
In the context of categories enriched in the category of partial order sets, we will work with KZ-reflectivity and Kan-injectivity, notions which, as we shall see, are closely related.We will show that there is an infinite chain of small subcategories of the category Top0, whose...
Lax orthogonal factorisation systems
2014-07-10
Speaker: Maria Manuel Clementino (CMUC)
In [4] Grandis and Tholen introduced natural weak factorisation systems (also called algebraic weak factorisation systems, see [3]) as pairs (L,R), where L is a comonad and R is a monad subject to suitable conditions, and showed that orthogonal factorisation systems are the natural weak...
Towards a calculus of fractions concerning Kan-injectivity
2014-06-24
Speaker: Lurdes Sousa (CMUC and IP Viseu)
In an order-enriched category $\cal X$, for a given subcategory $\cal A$, we study the class ${\cal A}^{KInj}$ of all morphisms with respect to which $\cal A$ is Kan-injective. We show that, for $\cal A$ an arbitrary subcategory of $\cal X$, ${\cal A}^{KInj}$ is, in a certain sense, closed...
The Karoubi envelope of sofic, Markov-Dyck and Property (A) shifts
2014-06-24
Speaker: Alfredo Costa (CMUC)
In this talk, we discuss some recent results, obtained jointly with Benjamin Steinberg, about the Karoubi envelope of the syntactic semigroup of a shift. We see that, in a natural way, the Karoubi envelope is the best possible syntactic invariant of flow equivalence of sofic shifts. ...
Trigroups and M-theory
2014-05-20
Speaker: John Huerta (CMAGDS, IST, Lisboa)
A trigroup is a tricategory with one object and all 1-, 2- and 3-morphisms invertible. M-theory is a mysterious branch of physics believed to unify the five 10D string theories and 11D supergravity. Without assuming any knowledge of physics, we will describe how the mathematics of M-theory...
Normality and its weaker forms
2014-04-08
Speaker: Mack Matlabyana (Univ. of Limpopo, South Africa)
In this talk we characterize normality and the weaker variants of normality by some quotient maps, namely, uplifting quotient maps, C1-quotient maps, R*- and G*-quotient maps....
Normal semicontinuous functions in pointfree topology and weak cb-frames
2014-04-08
Speaker: Imanol Mozo Carollo (Univ. of the Basque Country, Bilbao, Spain)
In a recent paper [2], we have constructed the Dedekind completion of the lattice C(L) of continuous real functions on a frame L, in terms of normal semicontinuous functions. Of course, this construction evokes the classical description of the completion of C*(X) (bounded continuous real...
Monoids and pointed S-protomodular categories
2014-03-18
Speaker: Andrea Montoli (CMUC, Univ. Coimbra)
We investigate the notion of pointed S-protomodular category, with respect to a suitable class S of split epimorphisms, and we show that these categories satisfy, relatively to the class S, many partial aspects of the properties of Mal'tsev and protomodular categories, like the split short...
Geodesic paths and weakly Mal'tsev categories
2014-03-18
Speaker: Nelson Martins Ferreira (CDRSP, ESTG, IP Leiria)
We introduce an algebraic structure with the purpose of modelling an arbitrary space with a suitable notion of geodesic path for every two points in it. We prove that this structure satisfies a weak Mal'tsev property, and show that any smooth surface in which every two points are linked by a...
Derivatives for equational theories and a special case of Taylor's conjecture
2014-01-09
Speaker: Luís Sequeira (CAUL, Univ. Lisboa)
The theory of Maltsev conditions has provided many useful characterizations of properties of varieties, like permutability or modularity of congruence lattices, by the satisfaction of certain identities. The notion of "derivative" for a an equational theory (or, equivalently,...
The set of equational classes of finitary functions on a finite set as a profinite semigroup
2014-01-09
Speaker: Jorge Almeida (CMUP, Univ. Porto)
For a fixed finite set A, we consider sets of finitary functions (or operations) on A, henceforth called classes. We are interested in such classes that can be defined by certain functional equations. It turns out that they constitute a semigroup under the natural notion of class...
On the contributions of lattice theory to the study of persistent homology.
2013-11-06
Speaker: João Pita Costa (Josef Stefan Institute, Liubliana, Slovenia)
In the past 20 years Topological Data Analysis has been a vibrant area of research a lot due to the developments in applied and computational algebraic topology. Essentially it applies the qualitative methods of topology to problems of machine learning, data mining or computer vision. Under...
What is a tensor product internally?
2013-10-15
Speaker:
Tim Van der Linden (Université Catholique de Louvain, Belgium)
When the concept of tensor product is studied from a categorical perspective, it is usually treated either as additional structure on a category - which leads to the theory of monoidal and enriched categories - or in an ad-hoc way involving free algebras of some kind. Quite surprisingly, as...
Remarks on reflexive multiplicative graphs in Gumm categories
2013-10-15
Speaker: Diana Rodelo (CMUC and Univ. Algarve)
A Gumm category is a finitely complete category where the categorical version of the Shifting Lemma holds. In varieties of universal algebras, the validity of this lemma is equivalent to being congruence modular. Mal'tsev and Goursat categories give examples of Gumm categories. We show that...
Double negation and other sites on monoides of sequences related to the convergence
2013-09-12
Speaker: Luis Espanol (Univ. de La Rioja, Logroño, Spain)
The abstract is in the attached pdf file....
The frame of partial reals and the Dedekind order completion of C(L)
2013-09-12
Speaker: Imanol Mozo Carollo (Univ. of the Basque Country, Bilbao, Spain)
Let L(R) denote the frame of reals [1], that is, the frame generated by all ordered pairs (p,q) of rationals, subject to the relations(R1) (p,q) ^ (r,s) = (p v r, q ^ s),(R2) (p,q) v (r,s) = (p,s) whenever p <= r < q <= s,(R3) (p,q) =V{(r,s) | p < r < s < q},(R4) V{(p,q) |...
Choice and Pointfree Topology
2013-06-18
Speaker: Bernhard Banaschewski (McMaster Univ., Hamilton, Canada)
Remarks on the interaction between pointfree topology and certain choice principles, specifically the Axiom of Choice (AC), the Axiom of Countable Choice (ACC), and the Boolean Prime Ideal Theorem (PIT), in connection with the following issues:(1) The equivalence of PIT with certain...
Non-pointed additive category
2013-06-04
Speaker: Dominique Bourn (U. Littoral, Calais, France)
The talk will deal with the study of the different degrees of non-pointed additiveness between Naturally Mal'cev categories (when the fibers of the fibration of points are additive) and essentially affine ones (when any change of base functor with respect with the same fibration is an...
Some semigroup-theoretic aspects of Rauzy graphs of subshifts
2013-05-22
Speaker:
Alfredo Costa (CMUC/Univ. Coimbra)
Symbolic dynamical systems, also called subshifts, correspond in a natural way to factorial prolongable languages. In this context, it is often relevant to study factor graphs, sometimes called Rauzy graphs, to which one gives a natural automaton structure. In this talk we first discuss the...
On the Beck-Chevalley condition for Set-monads
2013-03-26
Speaker: Maria Manuel Clementino (CMUC/Univ. Coimbra)
TBA...
Special completions of semilattices and lattices
2013-02-26
Speaker: Maria João Gouveia (Univ. Lisboa)
Canonical extensions of (bounded) lattices have been extensively studied, and the basic existence and uniqueness theorems for these have been extended to general posets. In this talk we will consider profinite completions of semilattices which may be identified with the iterated filter...
Sublattices of associahedra and permutohedra equations satisfied by associahedra
2013-02-26
Speaker: Luigi Santocanale (Univ. de Provence, France)
The set of permutations on n-elements is a poset when endowed with weak Bruhat ordering. Actually, this poset is a lattice since each finite subset of permutations has both a supremum and infimum. Such a lattice is known as the Permutohedron on n-elements. A strictly related lattice is...
On Alexander's Subbase Lemma
2013-01-15
Speaker: Dirk Hofmann (U. Aveiro)
Alexander's Subbase Lemma (due to James Waddell Alexander II) is a classical result of topology stating that a topological space X is compact provided that X is compact with respect to a subbasis, that is, every subbasic cover of X has a finite subcover. In this talk we will give a very...
Algebras, monoidal structures and cocycles
2012-11-27
Speaker: Dimitri Chikhladze (CMUC)
TBA...
Geometric semi-abelian categories
2012-07-18
Speaker: George Janelidze (U. Cape Town, South Africa)
TBA...
Normalizers and algebraic exponentiation
2012-07-18
Speaker: James Gray (UNISA, Pretoria, South Africa)
We recall the definition of algebraic exponents and their relationship to centralizers. We show that for action accessible categories the existence of normalizers implies that the category is fiberwise algebraically cartesian closed....
Dualities via splitting idempotents
2012-06-28
Speaker: Dirk Hofmann (U. Aveiro)
In 1994, R. Rosebrugh and R. Wood showed that the category of complete distributive complete lattices and suprema preserving maps is equivalent to the idempotent split completion of the category of sets and relations; and ten years later they observed that this result is not really...
Mal'cev products and the locality of pseudovarieties of semigroups
2012-04-24
Speaker: Ana Paula Escada (CMUC/Univ. Coimbra)
The global of a pseudovariety of semigroups V is the smallest pseudovariety of semigroupoids which contains V, where members of V are viewed as one-vertex semigroupoids. When the global of the pseudovariety V is characterized by properties of the local semigroups of its semigroupoids,...
De Morgan algebras: new perspectives and applications
2012-04-18
Speaker: H.P. Sankappanavar (State University of New York/CAUL)
It is well known that Boolean algebras can be defined using only the implication and the constant 0. It is, then, natural to ask whether De Morgan algebras can also be characterized using only a binary operation (implication) -> and a constant 0. In this lecture, I give an affirmative...
Complementing comonads
2012-03-20
Speaker: Craig Pastro (Kyushu University, Japan)
TBA...
Monoidal structures
2012-03-20
Speaker: Dimitri Chikhladze (CMUC)
TBA...
Mal'tsev categories and a generalised 3x3 Lemma
2012-02-28
Speaker: Diana Rodelo (CMUC/Univ. Algarve)
We prove that a regular category C is a Mal'tsev category if and only if a strong form of the denormalised 3x3 Lemma holds true in C....
Shreier Mac Lane theorem in the Mal'cev context
2012-02-28
Speaker: Dominique Bourn (Univ. du Littoral, Calais, France)
TBA...
Higher central extensions via binary commutators
2012-02-20
Speaker: Tim Van der Linden (Univ. catholique de Louvain, Belgium)
We prove that all semi-abelian categories with the Smith is Huq property satisfy the Commutator Condition: higher central extensions may be characterised in terms of binary (Huq or Smith) commutators. In fact, even binary Higgins commutators suffice. As a consequence, in presence of enough...
Semidirect products and split short five lemma in algebraic categories
2012-02-20
Speaker: Andrea Montoli (CMUC)
N. Martins Ferreira and M. Sobral proved that, in a pointed regular category C, the split epimorphisms are equivalent to the internal actions if and only if C is protomodular and every internal action is strict. We will show that, even if C is not protomodular, the regular split epimorphisms...
Topological space objects via neighbourhood systems
2012-02-20
Speaker: Nelson Martins-Ferreira (IP Leiria/CDRSP)
In this talk we consider the problem of defining a topological space object internal to an arbitrary category (perhaps with some extra structure, or appropriate conditions) in such a way that a topological space object in the category SET, of sets and maps, is a topological space, while, for...
Well-founded and well-pointed coalgebras
2012-01-20
Speaker: Lurdes Sousa (IP Viseu/CMUC)
A coalgebra (A,a) of an endofunctor H is well-founded if the square Hm.a'=a.m is not a pullback for any proper subcoalgebra m:(A',a')-->(A,A). For a graph, seen as a coalgebra of the power-set functor, this is exactly the usual definition of well-founded graph, as observed by G. Osius...
A Selection of Insertion-type results Extending Katetov's procedure
2011-11-23
Speaker: Javier Gutiérrez García (UPV, Bilbao, Spain)
TBA...
Normality vs. extremal disconnectedness: two sandwich-type results for the price of one
2011-11-23
Speaker: Jorge Picado (Mat.FCTUC/CMUC)
Several results in the literature about normal and extremally disconnected spaces (like Katetov-Tong type theorems, Uryshon's type lemmas or Tietze's type lemmas) shape the idea that the two notions are somehow dual to each other and therefore can be studied in parallel.In this talk we will...
Dualities in modal logics via the Kleisli construction
2011-09-20
Speaker: Dirk Hofmann (U. Aveiro)
Motivated by questions in semantics of modal (propositional) logics, over the past years several duality results were established which extend the classical Priestley and Stone dualities. In this talk we will show how the Kleisli construction for monads can simplify their proof and...
Baire sets and the Boolean reflection of sigma-frames
2011-06-30
Speaker: Bernhard Banaschewski (McMaster University, Canada)
For any topological space X, the σ-field BX of its Baire sets is the Boolean sub-σ-algebra of the power set of X generated by the σ-frame Coz X of the cozero sets of X. Apart from this, one obviously has the abstractly defined Boolean σ-frame reflection BCoz X and the...
On monotone normality and subfitness
2011-06-30
Speaker: Javier Gutiérrez García (Univ. Basque Country, Bilbao, Spain)
The notion of monotone normality was introduced in 1973 by Heath, Lutzer and Zenor as a strengthening of normality and is probably what you would guess if asked to define "normal in a monotone way". Every metrizable space and every linearly ordered space is monotonically normal. In...
Nonmeasurable cardinals and pointfree topology
2011-06-28
Speaker: Bernhard Banaschewski (McMaster University, Canada)
The familiar classical results that(i) any extremally disconnected P-space of nonmeasurable cardinal is discrete, and(ii) any discrete space of nonmeasurable cardinal is realcompactare shown to be consequences of much more general results concerning frames. The particular frames involved...
Injectivity and the fibrewise way-below relation
2011-06-28
Speaker: Maria Manuel Clementino (Mat.FCTUC/CMUC)
Using results of Escardó-Flagg [1] and Hofmann [2], we characterize continuous maps which are injective with respect to special classes of embeddings. These characterizations are based on a fibrewise way-below relation which generalizes the one used by Richter in his characterization...
Scott approach spaces
2011-03-29
Speaker: Gonçalo Gutierres (Mat. FCTUC/CMUC)
Approach spaces, introduced by R. Lowen in 1989, constitute a generalization of both topological and metric spaces. There are several ways of describing them, among the most common are the one using distances between points and sets, and the one using numerified convergence which tells how...
Approaching metric domains
2011-03-29
Speaker: Dirk Hofmann (U. Aveiro)
In analogy to the situation for continuous lattices which were introduced by Dana Scott as precisely the injective T_0 spaces via the (nowadays called) Scott topology, we study those metric spaces which correspond to injective T_0 approach spaces and characterise them as precisely the...
Semidirect products in Jonsson-Tarski varieties
2011-02-22
Speaker: Andrea Montoli (CMUC)
The aim of this talk is to characterize those split extensions corresponding to the classical semidirect product in Jonsson-Tarski varieties, with particular attention to the cases of monoids and unitary magmas, and to compare the classical notion of semidirect product with the categorical...
Internal categorical structures in weakly Mal'tsev categories
2011-02-22
Speaker: Nelson Martins-Ferreira (IP Leiria)
It is well known that in the context of a Mal'tsev category the three notions: multiplicative graph, internal category, internal groupoid; coincide and are completely determined by the respective underlying reflexive graph. In this talk we will see that in the more general case of a weakly...
A categorical invariant of flow equivalence
2011-01-25
Speaker: Alfredo Costa (Mat. FCTUC/CMUC)
The Karoubi envelope of a semigroup is a small category which plays a distinguished role in finite semigroup theory thanks to the Delay theorem of Tilson. In this talk, an application to the classification of symbolic dynamical systems is presented: up to natural equivalence, the Karoubi...
A mapping space for Gray-categories
2011-01-25
Speaker: Björn Gohla (U. Porto)
It is well known that connections on a principal G-bundle over a manifold M can be represented by group homomorphisms LM-->G, where LM is the loop group of M. Similarly, 2-connections can be seen as 2-functors from a 2-groupoid of points, paths and bigons in M to a 2-group G.In passing to...
On the number of finite algebras
2010-12-07
Speaker: Peter Mayr (CAUL)
In 1941 Emil Post showed that there are only countably many, essentially distinct algebraic structures of size 2. Here we consider two algebras as essentially the same (term equivalent) if they have the same term functions. As an example of term equivalent structures we may consider a...
Semidirect products of internal groupoids
2010-12-07
Speaker: Andrea Montoli (CMUC)
We give a characterization of those finitely complete categories with initial object and pushouts of split monomorphisms that admit categorical semidirect products. As an application we examine the case of groupoids with fixed set of objects. Further, we extend this to the internal...
Distributive law between a monad and a comonad
2010-11-09
Speaker: Ivan Yudin (CMUC)
This work is mainly motivated by the modern approach to the deformation theory of associative algebras.The idea is to unify notions of different <i>\infty</i>-algebras, such as <I>A<sub>\infty</sub></i>-algebras or...
A "one for the price of zero" duality principle for distributive spaces
2010-11-09
Speaker: Dirk Hofmann (U. Aveiro)
Our study of topological spaces presented as convergence structures shaped the ideathat "topological spaces are generalised orders", and eventually revealed thefollowing analogies. down-closed...
Resolutions, higher extensions and the relative Mal'tsev axiom
2010-09-14
Speaker: Tim Van der Linden (CMUC)
We study how the concept of higher-dimensional extension which comes from categorical Galois theory relates to simplicial resolutions and homology. For instance, an augmented simplicial object is a resolution if and only if its truncation in every dimension gives a higher extension, in which...
A Schreier-Mac Lane extension theorem in action accessible categories
2010-09-14
Speaker: Andrea Montoli (CMUC)
The aim of this talk is to give an intrinsic version of the Schreier-Mac Lane extension theorem, classically known for groups: on the set Ext(Y,K) of isomorphism classes of extensions with fixed abstract kernel there is a simply transitive action of the abelian group Ext(Y,ZK), where ZK is...
Internal categories in n-permutable varieties
2010-09-14
Speaker: Diana Rodelo (U. Algarve/CMUC)
We show that the notions of internal category and internal groupoid coincide for any n-permutable variety....
Daniell's version of Lebesgue integral II
2010-07-14
Speaker: Ales Pultr (Charles Univ., Prague, Czech Republic)
This is the second and last lecture of a short course on the integral introduced and developped by Percy John Daniell in his article "A general form of integral", Annals of Mathematics 19 (1918) 279-294.The course will consist on two lectures, 1h30m each.Lecture notes of the course...
Fibrewise injectivity and Kock-Zoberlein monads
2010-07-14
Speaker: Maria Manuel Clementino (Mat. FCTUC/CMUC)
In this talk we will apply the Theorem of Escardó-Flagg [2] characterizing injective objects as algebras for a Kock-Zoberlein monad to the characterization of injective morphisms, making use of a lifting of a Kock-Zoberlein monad to the corresponding slice categories. This result...
Daniell's version of Lebesgue integral I
2010-07-13
Speaker: Ales Pultr (Charles Univ., Prague, Czech Republic)
This is the first lecture of a short course on the integral introduced and developped by Percy John Daniell in his article "A general form of integral", Annals of Mathematics 19 (1918) 279-294.The course will consist on two lectures, 1h30m each.Lecture notes of the course may be...
Maximal subgroups of free profinite semigroups
2010-04-13
Speaker: Alfredo Costa (Mat.FCTUC/CMUC)
Free profinite semigroups proved to be a fundamental tool for the development of Finite Semigroup Theory since the mid 1980's. However, little is known about their structure. The first important advances were made in the last decade, based in a beautiful connection with symbolic dynamics...
Motives toward a pointfree study of completions of functorial (quasi)-uniformities on frames/locales
2010-03-23
Speaker: Guillaume Brummer (University of Cape Town, South Africa)
TBA...
Realizing modules over the homology of a DGA
2010-03-10
Speaker: Gustavo Granja (CAMGSD/IST)
Let A be a DGA over a field. A graded module X over H_*(A) is said to be realizable if there exists a DG module M over A with H_*(M)\cong X. There are at least two approaches to finding out whether a module is realizable. One uses Postnikov systems (certain diagrams in the derived category...
A homological hammer to pound an infinite problem into a finite calculation
2010-03-10
Speaker: Thomas Cassidy (Bucknell University, USA)
A list of generators and relations offers a succinct presentation for an algebra over a field, but what can we deduce when looking at this presentation? If two algebras have similar presentations, they may also share other characteristics. I will illustrate several ways in which...
Normalities and commutators
2010-02-23
Speaker: Sandra Mantovani (Universitá di Milano, Italy)
We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of this commutator. Our main result is to extend to any...
Folding up of monotone and concordant morphisms for sub-reflections from models in the category of presheaves
2010-02-23
Speaker: João Xarez (Universidade de Aveiro)
It will be presented a simplified version of the sufficient conditions for the concordant-dissonant and monotone-light factorizations to coincide, in the case of an adjunction from the category of presheaves on sets into a cocomplete category, satisfying the faithfulness of the composite of...
Remarks on two commutators
2009-11-24
Speaker: Tim Van der Linden (CMUC)
We show that two known conditions which naturally arose in commutatortheory and in the theory of internal crossed modules coincide: everystar-multiplicative graph is multiplicative if and only if every twoeffective equivalence relations commute as soon as so do theirnormalisations. This...
What are sifted colimits?
2009-11-10
Speaker: Jirí Adámek (TU Braunschweig, Germany)
Sifted colimits play in algebraic categories the analogous role that filtered colimits do in finitely presentable categories. A category D is called sifted if D-colimits commute with finite products in Set. Algebraic categories can be characterized as free completions of small categoris...
On étale morphisms in Algebra
2009-11-10
Speaker: Maria Manuel Clementino (CMUC/Mat. FCTUC)
The inclusion of every monadic category over Set in its category of relational algebras, which is topological over Set, suggests the study of topological notions in this algebraic setting. In this talk we will present the algebraic study and behaviour of étale morphisms in this...
Relative commutator theory and the associator of loops
2009-10-27
Speaker: Tim Van der Linden (CMUC/Mat. FCTUC)
The aim of this talk is to explain the concept of double central extension from the point of view of relative commutator theory. We shall focus on one concrete situation: the reflection of loops to groups. First we recall how the Galois theoretic approach to relative commutators arose out of...
Categories with colimits, 2-monads and Deligne's tensor product
2009-10-27
Speaker: Ignacio Lopez Franco (CMUC/Mat.FCTUC)
I'll explain how every lax idempotent (=KZ) 2-monad has a canonical structure of a pseudo-commutative 2-monad. In the case of the 2-monad R whose algebras are categories with finite colimits, this gives rise to a (pseudo) monoidal structure on R-Alg, corresponding to a pseudo-closed...
Local homeomorphisms in monadic categories
2009-09-22
Speaker: Maria Manuel Clementino (CMUC/Mat. FCTUC)
...
The equivalence between groupoids and crossed modules from a categorical point of view, with application in the case of groups
2009-09-22
Speaker: Nelson Martins-Ferreira (CDRSP/IPLeiria)
Starting with the well known equivalence of internal groupoids and crossed modules, in the case of groups, involving also the equivalence between points and actions, and the adjunction between actions by conjugation and semidirect products, we consider the problem of finding an appropriate...
On the representation of archimedean f-rings: extended versus pointfree functions
2009-07-21
Speaker: Bernhard Banaschewski (McMaster University, Canada)
A systematic comparison of the classical representation of archimedean f-rings with unit as l-rings of extended real-valued continuous functions (=allowing infinite values) on some compact Hausdorff spaces and their more recent representation as l-rings of real-valued continuous functions in...
On a generalization of Jordan algebras and other ternary algebras
2009-06-02
Speaker: Paulo Saraiva (CMUC/FEUC)
...
Satellites in Semi-Abelian Categories
2009-05-12
Speaker: Julia Goedecke (Centre for Mathematical Sciences, Univ. Cambridge, UK)
After giving a short introduction to semi-abelian categories, I will compare three different view-points of semi-abelian homology. The last of these uses the universal properties of a long exact homology sequence to make homology into a limit or pointwise Kan extension. This allows us to...
A groupoid approach to discrete inverse semigroup algebras
2009-04-27
Speaker: Benjamin Steinberg (Carleton Univ., Canada)
In is well known in the C*-algebra community that the C*-algebra of an inverse semigroup is an etale groupoid algebra. For finite inverse semigroups, the speaker showed that the semigroup algebra over any base commutative ring can be fruitfully viewed as a groupoid algebra. In this talk, we...
Categorical Groups
2009-02-10
Speaker: Björn Gohla (Mat. FCTUC)
Area(s): ...
Star-multiplicative graphs in pointed protomodular categories
2009-02-10
Speaker: Nelson Martins-Ferreira (CDRSP/IPLeiria)
Protomodularity, in the pointed case, is equivalent to the Split
Short Five Lemma. In this work we combine this and two other conditions on a
category B, in order to study and caracterize the relations between several
internal categorical structures in B, such as: groupoids,...
Compactified Picard stacks over the moduli space of curves with marked points
2008-12-22
Speaker: Ana Margarida Melo (CMUC/Mat. FCTUC and Università Roma Tre)
Let $X$ be a projective curve of genus $g$ and $Pic^d(X)$ its degree $d$
Picard variety, parameterizing isomorphism classes of invertible
sheaves of degree $d$ on $X$.
$Pic^d(X)$ is a very important invariant of the curve and it is well
known that it is complete if and only if $X$...
Galois theory and commutators
2008-12-02
Speaker: Tim Van der Linden (CMUC/Mat. FCTUC)
We explain how the relative commutator with respect to a
subvariety of a variety of omega-groups can be described in terms of
categorical Galois theory. This extends the known correspondence between
Fröhlich's and Janelidze and Kelly's notions of central extension.
Basing ourselves on...
Working with internal categories without pullbacks
2008-12-02
Speaker: Nelson Martins-Ferreira (CDRSP/IP Leiria)
The usual assumption to work with the notion of internal category
in some category C is the existence of pullbacks in C. In fact, a minimal
requirement is the existence of pullbacks of split epimorphisms along split
epimorphisms. In this note we will be interested in the notion of...
Simultaneously reflective and coreflective subconstructs
2008-10-31
Speaker: Robert Lowen ( University of Antwerp)
Area(s): ...
Analytic Functors
2008-10-21
Speaker: Jirí Adámek (TU Braunschweig, Germany)
Analytic functors of Andre Joyal, who considered them in the categories of
sets or vector spaces, are generalized to all symmetric
monoidal categories. Whereas for Set these are precisely the finitary
functors weakly preserving wide pullbacks, in other categories this
characterization...
A categorical construction of Gromov's metric
2008-07-08
Speaker: Maria Manuel Clementino (CMUC/Mat. FCTUC)
Area(s): ...
Internal precategories relative to split epis
2008-07-08
Speaker: Nelson Martins Ferreira (IP Leiria)
Area(s): ...
On locally bounded categories
2008-05-27
Speaker: Lurdes Sousa (CMUC/IP Viseu)
Area(s): ...
Configurations in and coproducts of Priestley spaces
2008-04-22
Speaker: Ales Pultr (Charles Univ., Prague, Czech Republic)
Priestley spaces are compact ordered order separated spaces; the famous Priestley duality links the resulting category with that of distributive lattices. The behaviour of finite connected subposets (configurations) in such a space reflects in algebraic, sometimes well-defined, properties of...
Continuous V-categories
2008-04-22
Speaker: Dirk Hofmann (Univ. Aveiro)
Area(s): ...
Morfismos de codescida efectiva de reticulados distributivos
2008-03-11
Speaker: Manuela Sobral (CMUC/Mat. FCTUC)
O problema central é a descrição dos morfismos de
de codescida efectiva na categoria dos reticulados distributivos
(=morfismos de descida efectiva na categoria dos espaços profinitos).
Com essa finalidade, descrevemos uma abordagem topológica e uma
abordagem algébrica. Condições...
Alguns aspectos algébricos de acções de álgebras de Hopf fracas
2008-03-11
Speaker: Christian Lomp (CMUP/U. Porto)
Acções de grupos, acções de álgebras de Lie e graduações de grupos finitos são
exemplos típicos de acções de álgebras de Hopf cujos propriedades foram estudados
durante muitos anos.
Em 1985 Cohen e Fishman levantaram a questão se o produto cruzado A#H de uma álgebra de Hopf semisimples...
Linear equivalent and identical Young tableau bijections for the conjugation symmetry of
Littlewood-Richardson coefficients
2008-02-29
Speaker: Ricardo Mamede (CMUC/Mat. FCTUC)
Benkart, Sottile, Stroomer and Fulton have completely
characterized a Young tableau bijection for the conjugation symmetry of the
Littlewood-Richardson coefficients
$c_{\mu,\nu}^{\gamma}=c_{\mu^t,\nu^t}^{\gamma^t}$ by Knuth and dual
Knuth equivalence. Tableau-switching,
the White...
Iterated periodicity in pseudowords over finite aperiodic semigroups
2008-02-29
Speaker: Jorge Almeida (CMUP/U. Porto)
We provide a characterization of pseudowords over the pseudovariety
of all finite aperiodic semigroups that are given by $\omega$-terms,
that is that can be obtained from the free generators using only
multiplication and the $\omega$-power. A necessary and sufficient
condition...
A universal construction in Goursat categories
2008-02-12
Speaker: Diana Rodelo (CMUC/U. Algarve)
We prove that the category of internal groupoids Grd(E) is a reflective subcategory of the category Rg(E) of internal reflexive graphs in a regular Goursat category E with coequalisers: this
implies that the category Grd(E) is itself regular Goursat. Area(s): ...
Using free profinite semigroupoids generated by Rauzy graphs
to compute J-maximal subgroups of free profinite semigroups
2008-01-08
Speaker: Alfredo Costa (CMUC/Mat. FCTUC)
Although free profinite semigroups proved to be a fundamental tool in the study of (pseudovarieties) of finite semigroups, their structure remained until recently significantly obscure. Jorge Almeida proposed to use some tools from symbolic dynamics to study them. In this talk we focus in...
How to deal with general real-valued functions in locales
2008-01-08
Speaker: Jorge Picado (CMUC/Mat. FCTUC)
Area(s): ...
Using approximation to characterize real computable functions
2007-12-17
Speaker: Manuel Campagnolo (DM/ISA/UTL e SQIG/IT)
In this talk the method of approximation to relate various classes of computable functions over the reals is reviewed. Using this method, Computable Analysis will be compared to two analog models: the
General Purpose Analog Computer and Real Recursive Functions. There are a number of...
Unidade e diversidade na teoria estrutural da demonstração
2007-11-27
Speaker: José Carlos Espírito Santo (Dep. Matemática, Univ. Minho)
A dedução natural e o cálculo de sequentes são dois dos principais sistemas de dedução formal usados e estudados em teoria estrutural da demonstração. A dedução natural manipula fórmulas, procura modelar o
raciocínio informal usado, por exemplo, nas demonstrações matemáticas, e tem relações...
Regular versus homological closure operators
2007-11-20
Speaker: Maria Manuel Clementino (CMUC/Mat. FCTUC)
In this talk we will compare results obtained by the speaker on weak heredity of regular closure operators on topological and abelian categories (cf. [2]), with recent results by Bourn-Gran [1] on weak heredity of homological closure operators on protomodular categories.
[1] D. Bourn, M....
System L: a linear version of Godel System T
2007-11-19
Speaker: Mário Florido (DCC, UP)
In this talk we present System L, a simple extension of the linear lambda calculus with Booleans, natural numbers and a linear iterator. We will show properties of this linear calculus and show the class of functions that can be represented. Surprisingly, this calculus is extremely...
The Tale of Three Entropies
2007-10-30
Speaker: Dikran Dikranjan
(Udine University, Italy)
To evaluate the ???chaos??? or ???disorder??? caused by a transformation T : K--K (preserving the natural structure of K) one defines the entropy of T.
The algebraic entropy of endomorphisms T : K--K of an abelian group
K was introduced by Adler, Konheim and McAndrew. In the same...
Étale groupoids as germ grupoids and their applications to coarse geometry
2007-10-23
Speaker: Dmitry Matsnev (IST)
Every étale topological groupoid G gives rise to an inverse semigroup equipped with a natural representation on the space of units of G. The germs of such representation can be given the structure of an étale groupoid which turns out to be isomorphic to G. We extend this...
Introdução ao Cálculo de Dedução Natural - análise dos conectivos
2007-10-15
Speaker: Gilda Ferreira (CMAF, UL)
O Cálculo de Dedução Natural, introduzido por Gerhard Gentzen em 1935 pretendendo aproximar-se o mais possível do modo de raciocínio humano, é ainda hoje um dos sistemas formais dedutivos mais conhecidos e estudados. Neste seminário propomo-nos introduzir, de modo sucinto, o Cálculo de...
The non-abelian counterpart of localisations
2007-09-18
Speaker: Maria Manuel Clementino
Area(s): ...
Some classes of factorizable semigroups
2007-06-12
Speaker: Gracinda Gomes (CAUL/Mat. FCUL)
[Almost] factorizable inverse monoids [semigroups] play an important rule in the theory of inverse semigroups (see for example [2]). The
notion of ???factorizable??? and ???almost factorizable??? coincides for inverse
monoids. A couple of crucial results for inverse semigroups S are...
Algebroids and 2-Ab-Categories
2007-05-25
Speaker: Nelson Ferreira (IP Leiria)
Area(s): Category Theory ...
The Orthogonal Subcategory and the Injective Subcategory Problems, and logics of morphisms
2007-05-25
Speaker: Lurdes Sousa (CMUC/IP Viseu)
Area(s): Category Theory ...
Ideals in Heyting semilattices: openness versus completeness under subfitness.
2007-04-20
Speaker: Jorge Picado (CMUC/Mat. FCTUC)
Area(s): Category Theory, Topology ...
The locality of some subpseudovarieties of DG
2007-03-27
Speaker: Ana Escada (CMUC/Mat. FCTUC)
The global of a pseudovariety of monoids is the pseudovariety of
categories generated by its elements when they are viewed as the
monoids of edges in one-vertex categories. The global of a
pseudovariety of monoids is useful to compute various
operators involving the...
Free Profinite Categories and Semigroupoids and how Symbolic Dynamics can help us to understand them
2007-03-13
Speaker: Alfredo Costa (CMUC/Mat. FCTUC)
(Work with Jorge Almeida)
Bret Tilson proposed in the 1987 paper
"Categories as algebra: an essential ingredient in the theory of monoids"
to see small categories and semigroupoids
as partial algebras generalizing the concepts of monoid and semigroup, respectively.
The results in...
Pointfree, but not pointless, approach theory
2007-01-31
Speaker: Christophe Van Olmen (CMUC/FCT)
Area(s): Category Theory, Topology ...
Towards a notion of T-frames
2007-01-31
Speaker: Dirk Hofmann (Dep. Mat, Univ. Aveiro)
Area(s): Category Theory ...
Torsion theories and Galois coverings of topological groups
2006-11-13
Speaker: Valentina Rossi (CMUC)
For any torsion theory in a homological category, one can define a categorical Galois structure and try to describe the corresponding Galois coverings.
We provide several characterizations of these coverings for a special class of torsion theories, that we call quasi-hereditary. These...
About Yoneda in T-categories
2006-11-13
Speaker: Dirk Hofmann (Univ. Aveiro)
Area(s): Category Theory ...
Admissible Galois structures and coverings in regular Mal'cev categories
2006-10-23
Speaker: Valentina Rossi (CMUC)
Given a regular Gumm category C such that any regular epimorphism is effective for descent, we prove that any Birkhoff subcategory X in C gives rise to an admissible Galois structure. This result allows one to consider some new applications of the categorical
Galois theory in the context of...
An algebraic approach to Turing machine computation
2006-10-17
Speaker: Pedro Silva (CMUP/Mat. Pura, FCUP)
We shall present a new approach to Turing machine computation based on profinite
limits of finite structures named bimachines. This is joint work with John
Rhodes (Berkeley).
Area(s): ...
Filippov superalgebras
2006-09-21
Speaker: Alexander Pozhidaev (Sobolev Inst Math, Sib. Branch Russian Acad. Sciences)
In this talk we will present some results on Filippov superalgebras which
are a very natural generalization of Lie algebras to the case of n-ary
operation of multiplication. We will show a connection of Filippov
superalgebras with Lie superalgebras and how to use it to classify...
Complete congruences on frames
2006-06-28
Speaker: Ales Pultr (Charles Univ., Prague)
Area(s): Category Theory, Topology ...
Implicit characterization of radicals
2006-06-06
Speaker: Jorge Almeida (CMUP / Matemática Pura, FCUP)
By a Fitting pseudovariety we mean a class of finite groups which is
closed under taking quotients and subgroups and such that, in every
finite group, the product of normal subgroups which lie in the class
also lies in the class. The associated radical of a finite group is
the product of...
O problema do contínuo - a solução parcial de Kurt Gödel
2006-06-01
Speaker: António Fernandes (IST, UTL)
Este seminário constitui uma abordagem ao problema do contínuo de Cantor e à solução parcial fornecida por Kurt Gödel, através do seu universo construtível. A abordagem será mais informal e conceptual que técnica. Area(s): Logic and Computation ...
Tiering without tears
2006-05-19
Speaker: Harold Simmons (Manchester)
Area(s): Logic and Computation ...
Identification of inconsistencies in low-level translations of user queries
2006-05-18
Speaker: Oliver Kullmann (Swansea)
Consider some complicated manufacturing process (producing for example a car, or a software component within a generative library), where not all orders can be fulfilled, but where the order has to be checked for inconsistency. In case the order is inconsistent (can not be fulfilled) we want...
Boolean reflections for frames
2006-05-16
Speaker: Harold Simmons (Manchester Univ., UK)
The category Frm of frames is an algebraic [point-free) modification of the category of topological spaces. In particular, each topology is a frame. A study of Frm gives us many algebraic techniques not available in the point-sensitive setting. The category Frm includes the category CBA of...
Abstract projective geometry and the origin of the logico-algebraic approach to quantum
theory
2006-03-07
Speaker: Isar Stubbe (CMUC, U. Coimbra)
I wish to present two most remarkable 'representation theorems' in the realm of
projective geometry: every arguesian projective geometry is represented by an essentially unique
vector space, and every arguesian Hilbert geometry is represented by an essentially unique
generalized Hilbert...
Congruências em Álgebras Dinâmicas
2006-02-07
Speaker: Teresa Martins (CMUC, U. Coimbra)
Para cada álgebra dinâmica separável, com elemento zero, D, iremos
estabeler uma ligação de Galois entre os reticulados CongD e IdeD,
respectivamente, das congruências dinâmicas e dos ideais dinâmicos definidos em D.
Area(s): ...
Completing functorial quasi-uniformities on spaces
2005-11-30
Speaker: Guillaume BrÌmmer (Univ. Cape Town)
Area(s): Topology, Category Theory ...
Sobre as álgebras de Malcev generalizadas
2005-10-18
Speaker: Paulo Saraiva (CMUC/Fac. Economia, UC)
Apresentamos uma generalização da noção de álgebra de Malcev (álgebras n-Malcev), bem como os resultados até agora conseguidos no estudo destas álgebras. Comparamos resultados com outros respeitantes às álgebras de Lie generalizadas (álgebras n-Lie ou álgebras de Filippov).
Area(s): ...
Quasi-equational Logic
2005-10-18
Speaker: Lurdes Sousa (CMUC/IPViseu)
Area(s): Category Theory ...
Torsion theories in normal categories
2005-09-20
Speaker: Maria Manuel Clementino (CMUC)
Area(s): Category Theory ...
Categorical structures enriched in a quantaloid: results, projects, ideas and dreams
2005-09-09
Speaker: Isar Stubbe (CMUC)
Being the new kid on the block at the CMUC, I shall use this first talk to present the subject that I intend to study during my post-doc in Coimbra the upcoming year. As the title indicates, it is all about the theory of categorical structures enriched in a quantaloid. I shall revise the...
Esquemas de recursão e classes de complexidade computacional
2005-05-03
Speaker: Isabel Oitavem
(Universidade Nova de Lisboa)
Neste seminário descrevem-se caracterizações implícitas de algumas classes
de complexidade computacional. As caracterizações aqui descritas são
expressas num contexto de álgebras livres. Isto permite-nos obter
caracterizações de classes tão diversas como Ptime, Lspace e NC mudando...
Étale groupoids and their quantales
2005-03-18
Speaker: Pedro Resende (Instituto Superior Técnico)
-- ...
Quantal sets over involutive quantales
2005-03-18
Speaker: Christopher J. Mulvey (Univ. of Sussex/Univ. of Cambridge, UK)
In this talk I shall report on work in progress with my student Joel Zamora Ramos of the University of Sussex on extending earlier work with Mohammad Nawaz on quantal sets over right Gelfand quantales. In doing so, I shall survey briefly the link between local sets and sheaves on a locale,...
Proof of the weak completeness of EQPL
2005-03-15
Speaker: Amílcar Sernadas (IST, Lisboa)
After a brief review of the language and semantics of EQPL (exogenous quantum propositional logic), a weak complete axiomatization is presented. The proof of completeness is achieved extending the Fagin-Halpern-Megiddo technique originally proposed in the context of probabilistic logic....
Invariantes de conjugação de sistemas dinâmicos simbólicos:
uma abordagem a partir da teoria de semigrupos profinitos.
2005-02-01
Speaker: Alfredo Costa (Universidade de Coimbra)
Exploramos algumas ligações entre a dinâmica simbólica e a teoria dos
semigrupos profinitos. Apresentamos três tipos de invariantes de conjugação de
sistemas dinâmicos simbólicos. Estes invariantes foram obtidos utilizando
métodos sintácticos da teoria dos semigrupos profinitos.
O...
Characterizing subgroups of the circle
2005-01-28
Speaker: Dikran Dikranjan (U. Udine, Italy)
Area(s): Topology, Category Theory ...
Priestley spaces: the threefold way
2005-01-28
Speaker: Manuela Sobral (CMUC)
Area(s): ...
A Galois Theory with stable units for simplicial sets
2005-01-11
Speaker: João Xarez (Univ. Aveiro)
Area(s): Category Theory ...
Closure operators in topological groups
2005-01-11
Speaker: Dikran Dikranjan (Univ. Udine, Italy)
Area(s): Topology, Category Theory ...
Paracategories and Saturated Partial Algebras
2004-11-12
Speaker: Claudio Hermida (Instituto Superior Técnico, Lisboa)
Freyd?s notion of paracategory embodies a system of morphisms subject to partial compositions. We give an abstract axiomatisation of this notion internally in a regular category admitting free monoids. This
leads us to consider the more general notion of partial algebras relative to a...
Condições de Maltsev e álgebras topológicas
2004-10-19
Speaker: Luís Sequeira
(Universidade de Lisboa)
Uma álgebra topológica é uma álgebra, equipada com uma topologia "compatível", isto é, para a qual as operações algébricas são contínuas.
Neste seminário, falaremos sobre como, em álgebras topológicas, propriedades algébricas condicionam as topologias compatíveis (e reciprocamente). ...
Sobre o estudo de álgebras lassas
2004-10-15
Speaker: Maria Manuel Clementino (CMUC)
Area(s): Category Theory ...
Group extensions and related categorical algebra revised
2004-06-22
Speaker: George Janelidze (Univ. of Cape Town)
Area(s): ...
Flat precovers in varieties
2004-05-18
Speaker: David Kruml
(Masaryk University, Brno, República Checa, e
IST, Lisboa)
In 2000,Bican, El Bashir and Enochs proved a conjecture that
every module has a flat (pre)cover. Flat objects can be defined in any
variety V as directed colimits of finitely presented projective objects
and then we can ask for an existence of flat precovers in V. We will start
with an...
Applicative Theories and their Applications
2004-04-27
Speaker: Reinhard Kahle
(Universidade de Coimbra)
Applicative Theories are the first order part of Feferman's systems of
Explicit Mathematics. They comprise type-free combinatory logic and
axiomatized natural numbers. In contrast to usual logic frameworks,
the underlying logic is partial, i.e., there is a special existence
predicate...
Dos grupos às álgebras semi-abelianas topológicas
2004-04-20
Speaker: Maria Manuel Clementino
(Universidade de Coimbra)
Neste seminário estudaremos as teorias algébricas semi-abelianas e introduziremos técnicas que permitem estender a álgebras semi-abelianas topológicas resultados clássicos dos grupos topológicos.
Area(s): ...
Mais notas sobre exponenciabilidade
2004-04-14
Speaker: Dirk Hofmann (Universidade de Aveiro)
Area(s): Category Theory ...
Teoremas de interpolação em topologia sem pontos
2004-03-30
Speaker: Jorge Picado
(Universidade de Coimbra)
Area(s): ...
Produtos topológicos em ZF
2004-03-04
Speaker: Gonçalo Gutierres da Conceição (CMUC)
Area(s): Topology, Set Theory ...
Combining logic systems: Why, how, what for?
2004-02-17
Speaker: Amílcar Sernadas
(Instituto Superior Técnico, Lisboa)
Motivated by applications in artificial intelligence and software
engineering that require the joint use of different deduction formalisms,
the interest in combination of logic systems has recently been growing, but
the topic is also of interest on purely theoretical grounds. Several...
A New Look at the Fundamental Theorem of Algebra
2004-01-20
Speaker: Luís Cruz-Filipe
(Centro de Lógica e Computação, IST, Lisboa)
In this talk we will explore one application of a constructive
formalization of the Fundamental Theorem of Algebra.
We begin by discussing the theoretical and practical interest of
formalizing mathematics, before a constructive proof of the FTA is
presented in detail. Then we look at...
Dentro e fora do filtro das variedades modulares
2003-11-18
Speaker: Luís Sequeira
(Universidade de Lisboa)
Um famoso teorema de Maltsev estabelece que, para
uma variedade V, a permutabilidade de
congruências em todas as álgebras de V é
equivalente à existência de um termo em V
satisfazendo duas simples identidades.
Muitos resultados posteriores vieram a
estabelecer condições...
Categorias de Moore
2003-10-21
Speaker: Diana Rodelo
(CMUC/Universidade do Algarve)
In 1970, M. Gerstenhaber introduced in [1] a list of axioms defining Moore categories in
order to develop the Baer Extension Theory. The independence of the axioms is studied
and they are compared with more recent notions. Thus, a Moore category is a pointed,
strongly protomodular and...
Terminal Coalgebras as Sets or Classes
2003-10-13
Speaker: Jirí Adámek (University of Braunschweig)
For endofunctors H of Set, coalgebras represent dynamical systems of the type expressed by H, and a terminal coalgebra T represents the collection of all possible behaviours of states of such systems.
This collection can be a class: not every set functor has a terminal coalgebra, but every...
Categorical approaches to connectedness
2003-09-23
Speaker: David Holgate (University of Stellenbosch, South Africa)
Area(s): Category Theory ...
New Galois structures from logic
2003-09-23
Speaker: George Janelidze (Georgian Academy of Sciencies, Tbilisi, Georgia)
Area(s): Category Theory ...
Cryptofibring
2003-06-17
Speaker: Carlos Caleiro (IST, Lisbon)
Although quite powerful, the fibring mechanism for combining logics suffers from an anomaly usually known as "the collapsing problem". In the first accounts of fibring it could be noticed that fibring a 2-valued with a 3-valued logic would yield no fibred 3-valued models, or that the fibring...
Relações entre a dinâmica de operadores implícitos e a estrutura de grupos finitos
2003-04-23
Speaker: Alfredo Costa
Area(s): ...
Boolean Galois Theories
2003-04-07
Speaker: George Janelidze (Georgian Academy of Sciencies, Tbilisi, Georgia)
Area(s): Category Theory ...
Álgebras planas, subobjectos puros e teorias de Von Neumann
2003-03-31
Speaker: Francis Borceux (Université Catholique de Louvain / CMUC)
Area(s): Category Theory ...
Os globais de duas subpseudovariedades de DA
2003-03-19
Speaker: Ana Paula Escada (CMUC)
Area(s): ...
Why coalgebras are (often) algebras
2003-03-10
Speaker: Hans-E. Porst (Univ. Bremen, Germany)
Area(s): Category Theory ...
Baer sums in Moore categories
2003-02-24
Speaker: Diana Rodelo (CMUC)
Area(s): Category Theory ...
Functorial quasi-uniformities and the Fletcher construction on frames
2003-02-10
Speaker: Jorge Picado (CMUC)
Area(s): Category Theory ...
On Galois Theory
2002-07-23
Speaker: G. Janelidze
Area(s): Category Theory ...
How accessible are categories of algebras?
2002-06-24
Speaker: Lurdes Sousa (CMUC)
Area(s): Category Theory ...
On the quasi-topos of reflexive lax algebras
2002-06-11
Speaker: Maria Manuel Clementino (CMUC)
Area(s): Category Theory ...
Various classes of effective descent maps in categories of lax algebras
2002-06-11
Speaker: Dirk Hofmann (Universidade de Aveiro)
Area(s): Category Theory ...
Algebraic operations and embeddings
2002-05-21
Speaker: John MacDonald (Univ. British Columbia, Vancouver, Canada)
Area(s): ...
Sobre uma caracterização de aplicações quociente em termos de ultrafiltros
2002-01-15
Speaker: Dirk Hofmann (Universidade de Aveiro)
Area(s): Category Theory ...
Sublocales via Heyting
2002-01-15
Speaker: Jorge Picado (CMUC)
Area(s): Category Theory ...
Estabilidade de imersões e subcategorias reflectivas de categorias monádicas geradas por espaços topológicos
2001-12-18
Speaker: Lurdes Sousa (CMUC)
Area(s): Category Theory ...
Espaços sequenciais e o Axioma da Escolha
2001-12-18
Speaker: Gonçalo Gutierres
Area(s): ...
Locally directed sets and domains
2001-12-04
Speaker: Ales Pultr (Charles Univ., Prague, Czech Republic)
In this seminar we describe various categories of domains, and similar categories, by means of a special transitive structure. Area(s): ...
Lax epimorphisms in Cat
2001-12-04
Speaker: Manuela Sobral
Area(s): Category Theory ...
Forbidden forests in Priestley spaces
2001-11-27
Speaker: Ales Pultr (Charles Univ., Prague, Czech Republic)
We characterize forbidden configurations in Priestley spaces by formulas concerning the corresponding distributive lattices. Area(s): ...
Espaços e funções exponenciáveis, II
2001-10-23
Speaker: Maria Manuel Clementino
Area(s): Category Theory ...
Some universal properties of the category of clones
2001-09-28
Speaker: Artur Barkhudaryan (Charles University, Prague, Czech Republic)
Our study was motivated by a problem of W. Taylor and O. C. Garcia about the breadth of the lattice of interpretability types of varieties. It shows that there exist arbitrarily large rigid sets of clones (which give antichains in the above lattice). Furthermore, every group can be...
General radical theory
2001-07-16
Speaker: László Márki (Academy of Sciences, Hungary)
Area(s): ...
Técnicas Algébricas em Indecidibilidade
2001-06-27
Speaker: Natália Rodrigues (IP Guarda, Portugal)
Area(s): ...
Indecidibilidade da Lógica dos Predicados
2001-05-30
Speaker: Maria Teresa Martins (CMUC)
Area(s): ...
Uniformidades em reticulados locais
2001-05-23
Speaker: Maria João Ferreira
Area(s): ...
Matrices, lax algebras, exponentiability and descent theory
2001-05-18
Speaker: Maria Manuel Clementino
Area(s): Category Theory ...
Non-abelian homological algebra I
2001-05-11
Speaker: George Janelidze (Univ. Aveiro)
Area(s): Category Theory ...
Sobre o Teorema da Completude
2001-05-02
Speaker: Sandra Pinto
Area(s): ...
Álgebras dinâmicas
2001-04-27
Speaker: Maria do Céu Pinto
Area(s): ...
Centrality and Internal Structures in Universal Algebra
2001-03-14
Speaker: Marino Gran (Univ. Catholique Louvain, Belgium)
A variety of universal algebras is Maltsev if it has a ternary term p(x,y,z) satisfying the axioms p(x,y,y)=x and p(x,x,y)=y. Accordingly, the varieties of groups, rings, Lie algebras, quasigroups, crossed modules and Heyting algebras are all examples of Maltsev varieties. We shall first...
Topological examples of lax algebras
2001-02-14
Speaker: Dirk Hofmann (Univ. Coimbra, Portugal)
Area(s): ...
O expoente de potência de uma pseudovariedade de semigrupos
2001-02-14
Speaker: Ana Paula Escada
Area(s): ...
Quantal spaces
2001-02-09
Speaker: Christopher Mulvey (University of Sussex, UK)
One of the principal reasons for the introduction of the concept of quantale was to find a categorical context, generalising to the non-commutative case that of locales, within which the insights of Giles and Kummer into the spectral representation of C*-algebras might be placed....
Iteration monads: a coalgebraic approach to infinite computation
2001-01-10
Speaker: Jirí Adámek (Technical Univ. Braunschweig, Germany)
Area(s): ...
Coherence via Universality
2000-11-24
Speaker: Claudio Hermida (IST, Lisboa, Portugal)
In this talk we present our papers [1] and [2], trying to give an overall picture while illustrating with the main example taken from the first paper.
[1] From coherent structures to universal properties (to appear in Journal of Pure and Applied Algebra)
Abstract: Given a 2-category K...
Topological descent theory via lax algebras over monads
2000-11-10
Speaker: George Janelidze (Universidade de Aveiro, Portugal)
Area(s): ...
Central extensions in semi-abelian categories
2000-11-10
Speaker: Marino Gran (Univ. Catholique Louvain, Belgium)
Area(s): ...
Normality and centrality in protomodular categories
2000-10-25
Speaker: Marino Gran (Univ. Catholique Louvain, Belgium)
Area(s): ...
Finite étale-descent
2000-10-11
Speaker: Manuela Sobral
Area(s): ...
Limit stability of classes of quotient maps
2000-09-27
Speaker: Dirk Hofmann (Universidade de Coimbra, Portugal)
Area(s): ...
Characterization of topological exponentiable maps via convergence
2000-09-13
Speaker: Maria Manuel Clementino
Area(s): Category Theory ...
Compactness and the Axiom of Choice
2000-07-26
Speaker: Gonçalo Gutierres
Area(s): ...
Algumas considerações sobre dualizabilidade
2000-06-28
Speaker: Maria João Saramago (C.A.U.L. - Universidade de Lisboa, Portugal)
Uma álgebra finita M diz-se dualizável se existir uma estrutura topológica operacional e relacional (M; G, H, R, \tau) que forneça à quase-variedade A gerada por M uma dualidade natural. A questão que abordaremos é a da caracterização das álgebras finitas dualizáveis. Em particular,...
Quantum logic: Overview, intuitionistic perspective, dynamical/categorical developments
2000-06-19
Speaker: Bob Coecke (Free University of Brussels, Belgium)
Area(s): ...
Characterizations of special classes of quotient maps via convergence II
2000-05-10
Speaker: Dirk Hofmann (Universidade de Coimbra, Portugal)
Area(s): Category Theory ...
Characterizations of special classes of quotient maps via convergence I
2000-05-10
Speaker: Maria Manuel Clementino
Area(s): Category Theory ...
Decision problems for trace semigroups
2000-04-19
Speaker: Michal Kunc (Masaryk Univ., Brno, Czech Republic)
Area(s): ...
Unification in varieties of semigroups
2000-04-13
Speaker: Libor Polak (Masaryk Univ., Brno, Czech Republic)
Area(s): ...
Algebra for modelling homotopy n-types
2000-04-13
Speaker: Tim Porter (Univ. Wales, Bangor, UK)
Area(s): ...
Aros totalmente ordenados: um exemplo de Álgebras da Lógica
2000-03-29
Speaker: Isabel Ferreirim (Univ. Lisboa)
Area(s): ...
Quantales, noncommutative topology and observable properties of systems
2000-03-15
Speaker: Pedro Resende (Instituto Superior Técnico, Lisboa)
Area(s): ...
On a generalized Stone-Weierstrass theorem and its application to natural dualities
2000-02-10
Speaker: Dirk Hofmann (CMUC)
Area(s): ...
Normal subobjects in protomodular categories
2000-01-18
Speaker: Dominique Bourn (Univ. du Littoral, Calais, France)
Area(s): ...
A criterion for a completely regular frame to have a locally connected compactification
2000-01-05
Speaker: Dharmanand Baboolal (University of Durban, South Africa)
Area(s): ...
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