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Essentially surjective functor information


In mathematics, specifically in category theory, a functor

is essentially surjective if each object of is isomorphic to an object of the form for some object of .

Any functor that is part of an equivalence of categories is essentially surjective. As a partial converse, any full and faithful functor that is essentially surjective is part of an equivalence of categories.[1]

  1. ^ Mac Lane (1998), Theorem IV.4.1

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