Characterization of coextensive varieties of universal algebras

Description:  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 S.Schanuel, although "categories with disjoint and universal coproducts" were considered by A. Grothendieck a long time ago, and there are related papers of various authors. A motivating example of a coextensive category is the category CRing of commutative rings, which leads one to ask which varieties of universal algebras are coextensive. In this talk we answer this question by giving a syntactical characterization of coextensive varieties of universal algebras. Date:  2020-11-10 Start Time:   16:00 Speaker:  David Neal Broodryk (University of Cape Town, South Africa) Institution:  University of Cape Town Research Groups: -Algebra, Logic and Topology See more:   <Main>