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A groupoid is a category where every morphism is an isomorphism. Taking its skeleton throws the baby with the water, as you are left with a category where the only morphisms there are the identities no morphisms between different objects, i.e., a bunch of the objects..groups or a diagonal groupoid.

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A groupoid is a category where every morphism is an isomorphism. Taking its skeleton throws the baby with the water, as you are left with a category where the only morphisms are the identities of the objects...