#
Characterization of left coextensive varieties of universal algebras

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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.

http://www.tac.mta.ca/tac/volumes/34/32/34-32.pdf

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