Definition:Split Epimorphism

Definition
Let $\mathbf C$ be a metacategory.

Let $f: C \to D$ be a morphism of $\mathbf C$.

Then $f$ is said to be a split epimorphism iff for some $g: D \to C$, one has:


 * $f \circ g = \operatorname{id}_D$

where $\operatorname{id}_D$ is the identity morphism of $D$.

That is, iff $f$ has a section.

Also see

 * Split Epimorphism is Epic, justifying terminology
 * Split Monomorphism