= Equivalence of categories
An equivalence consists of <functors> $F:\mathcal C\to\mathcal D$ and $G:\mathcal D\to\mathcal C$ with <natural transformation> isomorphisms $GF\cong1_{\mathcal C}$ and $FG\cong1_{\mathcal D}$. A <full and faithful functor> which is essentially surjective, meaning every target object is isomorphic to an image object, is part of an equivalence under the usual choice convention. An isomorphism of categories is stronger: it has a strictly inverse functor.
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