Relaxed actions of monoids: Towards a new cohomology theory
 
 
Description:  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 its complement. Indeed these are both orthogonal special cases of a single construction in the category of monoids.

In this talk we discuss this construction and the related notion of a 'relaxed action' of monoids. We will explore an analogue of the second cohomology group parameterised by these relaxed actions. We will see that the associated monoid extensions generalise a number of classes of extensions that already exist in the literature. Finally we will discuss how these ideas may be extended to a full cohomology theory.
Date:  2021-01-05
Start Time:   16:00
Speaker:  Peter Faul (University of Cambridge, UK)
Institution:  University of Cambridge
Research Groups: -Algebra, Logic and Topology
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© Centre for Mathematics, University of Coimbra, funded by
Science and Technology Foundation
Financiado total ou parcialmente pela FCT, Fundação para a Ciência e a Tecnologia, I.P., sob o Financiamento de:
Projeto Estratégico com a referência DOI UID/00324/2025.   https://doi.org/10.54499/UID/PRR/00324/2025     UID/PRR/00324/2025   https://doi.org/10.54499/UID/PRR2/00324/2025   UID/PRR2/00324/2025
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