Definition:User:Dfeuer/Renaming Mapping/Definition 2
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Let $S, T$ be sets.
Let $\mathcal R$ be an equivalence relation on $S$.
Let $f: S \to T$ be any mapping.
Let $q_\mathcal R: S \to S / \mathcal R$ be the quotient mapping induced by $\mathcal R$.
Suppose that there is a mapping $r: S / \mathcal R \to T$ such that:
- $r \circ q_\mathcal R = f$
Then $r$ is called the renaming mapping.