The

**canonical set epimorphism**

*to*$X / {\sim}$ is the D18: Map \begin{equation} X \to X / {\sim}, \quad x \mapsto {\sim}(x) \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Relation class

▾ Set of relation classes

▾ Quotient set

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Relation class

▾ Set of relation classes

▾ Quotient set

Formulation 0

Let $X / {\sim}$ be a D180: Quotient set.

The**canonical set epimorphism** *to* $X / {\sim}$ is the D18: Map
\begin{equation}
X \to X / {\sim}, \quad
x \mapsto {\sim}(x)
\end{equation}

The

Formulation 1

Let $X / {\sim}$ be a D180: Quotient set.

The**canonical set epimorphism** *to* $X / {\sim}$ is the D18: Map
\begin{equation}
X \to X / {\sim}, \quad
x \mapsto \{ y : (x, y) \in {\sim} \}
\end{equation}

The

Also known as

Canonical surjection

Results