Definition:Split Monomorphism

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 monomorphism iff for some $g: D \to C$, one has:


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

where $\operatorname{id}_C$ is the identity morphism of $C$.

Also see

 * Split Monomorphism is Monic, justifying terminology
 * Split Epimorphism