Essentially surjective functor

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In mathematics, specifically in category theory, a functor

F:CD

is essentially surjective if each object d of D is isomorphic to an object of the form Fc for some object c of C.

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]

Notes

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

References