Essentially surjective functor

In mathematics, specifically in category theory, a functor 
is essentially surjective (or dense) if each object formula_2 of formula_3 is isomorphic to an object of the form formula_4 for some object formula_5 of formula_6.
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.