Polyadic sets and unnatural isomorphisms

Description:  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 polyadic sets, and explain their relation to homomorphism counting results in mathematics and finite model theory. A typical result of this type states that two representable presheaves are naturally isomorphic whenever they are unnaturally (i.e., pointwise) isomorphic. For example, two (finite) graphs are isomorphic precisely when they admit the same number of homomorphisms from any other graph (Lovász, 1967). Date:  2023-03-14 Start Time:   15:00 Speaker:  Luca Reggio (University College London, UK) Institution:  University College London, UK Place:  Sala 2.5, DMUC Research Groups: -Algebra, Logic and Topology See more:   <Main>