= Isomorphism of categories
An isomorphism of <categories> is a <functor> with a strictly inverse <functor>. It is equivalently bijective on objects and on each hom-set. An <equivalence of categories> only requires inverse composites up to invertible <natural transformations>. For example, the <category of partial functions> and the <category of pointed sets> are equivalent but their actual object collections prevent an isomorphism: the former has one <zero object>, the empty <set>, while the latter has distinct singleton <pointed set> objects that are all zero objects.
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