Congruence permutability in quasivarieties

TL;DR

This paper demonstrates that a natural form of congruence permutability in quasivarieties necessarily implies they are varieties, clarifying a theoretical relationship with a concise proof.

Contribution

It explicitly states and proves that congruence permutability in quasivarieties implies they are varieties, clarifying a previously implicit relationship.

Findings

Congruence permutability in quasivarieties implies they are varieties.

The result follows directly from existing literature.

The paper provides a concise proof of this implication.

Abstract

It is shown that a natural notion of congruence permutability for quasivarieties already implies ``being a variety''. The result follows immediately from [3] and the sole aim of this note is to state it explicitly, together with a telegraphic proof.