## Congruence uniformity

An algebra is \emph{congruence uniform} if for all congruence relations $\theta$ of the algebra it holds that all congruence classes of $\theta$ have the same cardinality.

A class of algebras is \emph{congruence uniform} if each of its members is congruence uniform.

Congruence uniformity holds for many 'classical' varieties such as groups, rings and vector spaces.

This property can be characterized by a Mal'cev condition …