Definition:Invariant Mapping Under Equivalence Relation

Definition
Let $S$ and $T$ be sets.

Let $\mathcal R$ be an equivalence relation on $S$.

Let $f: S \to T$ be a mapping.

Then $f$ is invariant under $\mathcal R$ :
 * $x \mathrel {\mathcal R} y \implies f \left({x}\right) = f \left({y}\right) $

Also see

 * Universal Property of Quotient Set