# Characterization of left coextensive varieties of universal algebras

## David Neal Broodryk

An extensive category can be defined as a category C with finite coproducts such that for each pair X,Y of objects in C, the canonical functor $+ : C/X \times C/Y \to C/(X + Y)$ is an equivalence. We say that a category C with finite products is left coextensive if the dual canonical functor $\times : X/C \times Y/C \to (X \times Y)/C$ is fully faithful. We then give a syntactical characterization of left coextensive varieties of universal algebras.

Keywords: Coextensivity, Universal Algebra, Syntactic Characterization

2010 MSC: 18A30, 08B05

Theory and Applications of Categories, Vol. 34, 2019, No. 32, pp 1036-1038.

Published 2019-10-18.

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