In mathematics, specifically in category theory, a functor
F : C → D {\displaystyle F:C\to D}is essentially surjective if each object d {\displaystyle d} of D {\displaystyle D} is isomorphic to an object of the form F c {\displaystyle Fc} for some object c {\displaystyle c} of C {\displaystyle 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.
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Notes
- Mac Lane, Saunders (September 1998). Categories for the Working Mathematician (second ed.). Springer. ISBN 0-387-98403-8.
- Riehl, Emily (2016). Category Theory in Context. Dover Publications, Inc Mineola, New York. ISBN 9780486809038.
External links
References
Mac Lane (1998), Theorem IV.4.1 ↩