# Definition:Section (Category Theory)

## Contents

## 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

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

## Sources

- 1965: Barry Mitchell:
*Theory of Categories* - 2010: Steve Awodey:
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