Diagonal Relation is Universally Congruent

Theorem
The diagonal relation $$\Delta_S$$ on a set $$S$$ is universally congruent with every operation on $$S$$.

Proof
An equivalence relation which is compatible with an operation is by definition a congruence relation.

The Diagonal Relation is Universally Compatible and also an equivalence relation

It can therefore be described as a universally congruent.