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}

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}