Equivalence relation/Canonical projection/Definition

Let ${\displaystyle {}R\subseteq M\times M}$ denote an equivalence relation, and let ${\displaystyle {}M/R}$ be the quotient set. The mapping

${\displaystyle q_{R}\colon M\longrightarrow M/R,x\longmapsto [x],}$

is called the canonical projection of ${\displaystyle {}R}$.