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.