Essentially surjective functor

In mathematics, specifically in category theory, a functor

$F:C\to D$

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.

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