#
nLab
inverse functor

Contents
### Context

#### Category theory

**category theory**

## Concepts

## Universal constructions

## Theorems

## Extensions

## Applications

# Contents

## Idea

The concept of *inverse functor* is the generalization of that of *inverse function* from sets to categories. Where the existence of an inverse function exhibits a bijection of sets, the existence of an inverse functor exhibits an equivalence of categories.

## Definition

Given a functor

$F \;\colon\; \mathcal{C} \longrightarrow \mathcal{D}$

then an *inverse* to $F$ is a functor going the other way around

$G \;\colon\; \mathcal{D} \longrightarrow \mathcal{C}$

together with natural isomorphisms relating their composites to the respective identity functors:

$G\circ F \simeq id_{\mathcal{C}}
\phantom{AAAA}
F \circ G \simeq id_{\mathcal{D}}
\,.$

Created on July 2, 2017 at 13:22:54.
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