Congruence distributivity
An algebra is \emph{congruence distributive} (or CD for short) if its lattice of congruence relations is a distributive lattice.
A class of algebras is \emph{congruence distributive} if each of its members is congruence distributive.
Congruence distributivity has many structural consequences. The most striking one is perhaps Jónsson's Lemma 1) which implies that a finitely generated CD variety is residually finite.