nLab inverse functor




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.


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 13:22:54. See the history of this page for a list of all contributions to it.