In mathematics, specifically in category theory, a functor
\( F:C\to D
is essentially surjective (or dense) 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.[1]
Notes
Mac Lane (1998), Theorem IV.4.1
References
Mac Lane, Saunders (September 1998). Categories for the Working Mathematician (second ed.). Springer. ISBN 0-387-98403-8.
External links
Essentially surjective functor in nLab
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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