Skeletal category

Skeletal categories are equivalent iff they are isomorphic

Let be skeletal categories. Then these are isomorphic iff they are equivalent, #m/thm/cat/evil i.e.

Proof

Suppose defines an equivalence of categories. Then there exist natural isomorphisms and , which must be identities since and are skeletal.

This is a lemma for the stronger Categories are equivalent iff they have isomorphic skeleta.

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