Split Epimorphism

A morphism $r:{{X}\to{Y}}$ in a Category $\mathcal{C}$ is a split epimorphism there is some other $s:{{Y}\to{X}}$ with $r\circ s=mathrm{id}{ifx..lse\par i}$.

Properties

• Every split epimorphism is Epic.

• If $f\circ g$ is split epic, then $g$ is split epic.

• The axiom of choice says that every epimorphism in the Category of Sets is split.