Definition:Split Epimorphism

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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 if and only if 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, if and only if $f$ has a section.

Also see