## You are here

Homeretract

## Primary tabs

# retract

*retract* of $X$ and $r$ is a *retraction*.

Defines:

retraction

Related:

DeformationRetraction, PeriodOfMapping

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

54C15*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections

## Comments

## Retracts are defined for any category

Hi

The concept of a retract is not specific to topological spaces, it is defined for any category as an object which is the target of a retraction (left inverse morphism). I think the article should cover the general definition and provide several examples including the topological case.

## Re: Retracts are defined for any category

Alternatively, you might want to instead an entry to the

existing one which explains the points you just made about

how this concept of retract generalizes.