# 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.