Definition:Relation Compatible with Operation

Definition
Let $$\mathcal R$$ be a relation on an algebraic structure $$\left({S, \circ}\right)$$.

Then $$\mathcal R$$ is compatible with $$\circ$$ iff:


 * $$\forall x_1, x_2, y_1, y_2 \in S: x_1 \mathcal R x_2 \and y_1 \mathcal R y_2 \implies \left({x_1 \circ y_1}\right) \mathcal R \left({x_2 \circ y_2}\right)$$

Also see

 * Congruence relation