Definition:Invariant Mapping Under Equivalence Relation

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

Let $\RR$ be an equivalence relation on $S$.

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

Then $f$ is invariant under $\RR$ :
 * $x \mathrel \RR y \implies \map f x = \map f y$

Also see

 * Universal Property of Quotient Set