Essentially surjective functor

In mathematics, specifically in category theory, a functor

is essentially surjective (or dense) 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


  • Mac Lane, Saunders (September 1998). Categories for the Working Mathematician (second ed.). Springer. ISBN 0-387-98403-8.
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