A syntactical and categorical analysis for Varieties with Right Existentially Defined Factor Congruences

TL;DR

This paper explores the properties of varieties with Right Existentially Definable Factor Congruences, establishing equivalences among definability, stability, and coextensivity of certain algebraic properties.

Contribution

It provides a syntactical and categorical analysis demonstrating the equivalence of key properties in these algebraic varieties.

Findings

Definability of complementary central elements is equivalent to stability by complements.

Stability by complements is equivalent to coextensivity in the algebraic category.

The paper offers a unified view of these properties in the context of Right Existentially Definable Factor Congruences.

Abstract

In this paper we prove that in the context of varieties with Right Existentially Definable Factor Congruences, definability of the property "e and f are complementary central elements", stability by complements and coextensivity of its respective algebraic category, are equivalent.