Skeletal category

Skeletal categories are equivalent iff they are isomorphic

Let be skeletal categories. Then these are isomorphic iff they are equivalent, cat 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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