# Symbols:Q/Quotient Mapping

## Quotient Mapping

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

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 .