nLab
inverse functor

Contents

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:𝒞𝒟 F \;\colon\; \mathcal{C} \longrightarrow \mathcal{D}

then an inverse to FF is a functor going the other way around

G:𝒟𝒞 G \;\colon\; \mathcal{D} \longrightarrow \mathcal{C}

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

GFid 𝒞AAAAFGid 𝒟. 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.