Essentially surjective functor
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In mathematics, specifically in category theory, a functor
is essentially surjective 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]
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
![]() | Original source: https://en.wikipedia.org/wiki/Essentially surjective functor.
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