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In the theory of 2-categories, we have the following theorem. A pseudofunctor is an equivalence of 2-categories if it is essentially surjective on objects, and the induced functor on Hom categories is an equivalence. I believe this is a well known result, does anyone know where it is contained that I may reference it?

Thanks in advance

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Have a look at http://arxiv.org/abs/1211.1877v1. I believe this is Proposition 1.6.

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