# Symbols:Q/Quotient Mapping

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## Quotient Mapping

- $q_\RR$

The **quotient mapping induced by $\RR$**:

- $q_\RR: S \to S / \RR: \map {q_\RR} s = \eqclass s {\RR}$

where:

- $\RR \subseteq S \times S$ be an equivalence relation on a set $S$

- $\eqclass s \RR$ is the $\RR$-equivalence class of $s$

- $S / \RR$ is the quotient set of $S$ determined by $\RR$.

Also known as:

- the
**canonical surjection**from $S$ to $S / \RR$ - the
**canonical map**or**canonical projection**from $S$ onto $S / \RR$ - the
**natural mapping**from $S$ to $S / \RR$ - the
**natural surjection**from $S$ to $S / \RR$ - the
**classifying map**or**classifying mapping**(as it*classifies*the elements of $S$ into those various equivalence classes) - the
**projection**from $S$ to $S / \RR$

The $\LaTeX$ code for \(q_\RR: S \to S / \RR\) is `q_\RR: S \to S / \RR`

.