Definition:Split Epimorphism
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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 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
- Split Epimorphism is Epic, justifying terminology
- Definition:Split Monomorphism
Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 2.1.1$: Definition $2.7$