Mal'cev condition

Summary

A Mal'cev condition is a property of a variety that asserts the existence of terms satisfying certain identities. Many properties of the congruence lattices of all algebras in a variety are equivalent to Mal'cev conditions. Examples are congruence permutability, given by a Mal'cev term, congruence distributivity, given by Jónsson terms, and congruence modularity, given by Day terms. Mal'cev conditions turn questions about all algebras of a variety into questions about finitely many equations.