When are exact categories co-exact?
 
 
Description: 

The aim of the talk is two-fold:

(i) to explain that finitely co-complete pretoposes are co-ideally-exact [J] and co-arithmetical [P], and (ii) to explain that there are conditions in common between additive and lextensive categories, which together with exactness (and finite cocompleteness) imply co-exactness and co-protomodularity. As a consequence of (i), we recover Theorem 1.3 of [BC], which states that the dual of the category of pointed compact Hausdorff spaces is semi-abelian, which in fact was the motivation to begin this work.

References:
[BC] F. Borceux, M.M. Clementino, On toposes, algebraic theories, semi-abelian categories and compact Hausdorff spaces, Theory and Applications of Categories 43(11), 363-381, 2025.
[J] G. Janelidze, Ideally exact categories, Theory and Applications of Categories 41(11), 414-425, 2024.
[P] M.C. Pedicchio, A categorical approach to commutator theory, Journal of Algebra 177, 647-657, 1995.

Date:  2025-10-07
Start Time:   15:00
Speaker:  James Gray (Stellenbosch Univ., South Africa)
Institution:  Stellenbosch University, South Africa
Place:  Online: https://flnlucatelli.github.io/ONLINEALTSEMINAR.html
Organization:  Fernando Lucatelli Nunes
URL:  https://flnlucatelli.github.io/ONLINEALTSEMINAR.html
See more:   <Main>   <Algebra, Logic and Topology (online)>  
 
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