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category theory

# 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 09:22:54. See the history of this page for a list of all contributions to it.