Characterization of coextensive varieties of universal algebras

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. In this thesis we give a syntactic characterization of coextensive varieties of universal algebras. We first show that any such variety must have what we call a diagonalizing term. The existence of such a term is a Mal'tsev condition which is interesting in its own right, and we show that it is sufficient to prove many useful subconditions of coextensivity. We also introduce the notion of a category with upward closed subproducts as a categorical generalization of varieties with diagonalizing terms, which we study in the more general context of Barr-exact categories.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2025

Author dc:creator

• Broodryk, David Neal

Advisors dc:contributor.advisor

• Janelidze, George
• Janelidze-Gray, Tamar

• Algebras
• Mathematics

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/11427/42120

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/42120