# Definition:Retraction

## Definition

Let $\mathbf C$ be a metacategory.

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

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

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

### Retract

Let $g: D \to C$ be a retraction of $f$.

Then $D$ is said to be a retract of $C$.