Definition:Section (Category Theory)

Definition
Let $\mathbf C$ be a metacategory.

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

A section of $f$ is a morphism $g: D \to C$ such that:


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

Also known as
Some authors refer to this as a coretraction.

Also see

 * Definition:Split Epimorphism, a morphism admitting a section
 * Definition:Retraction, the name for $f$ in the same situation, from the viewpoint of $g$