Characterization of coextensive varieties of universal algebras II

TL;DR

This paper provides a syntactical characterization of coextensive varieties of universal algebras, enhancing the understanding of their structural properties within category theory.

Contribution

It offers a new syntactical criterion for identifying coextensive varieties of universal algebras, building on previous categorical characterizations.

Findings

Characterization of coextensive varieties using syntax

Extension of categorical concepts to algebraic varieties

Updated theoretical framework for algebraic coextensiveness

Abstract

A coextensive category can be defined as a category $\mathcal{C}$ with finite products such that for each pair $X,Y$ of objects in $\mathcal{C}$, the canonical functor $\times\colon X/\mathcal{C} \times Y/\mathcal{C} \to (X \times Y)/\mathcal{C}$ is an equivalence. We give a syntactical characterization of coextensive varieties of universal algebras. This paper is an updated version of the pre-print arXiv:2008.03474