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.