Essentially surjective 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.
- 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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