Essentially surjective functor
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.
- Riehl, Emily (2016). Category Theory in Context. Dover Publications, Inc Mineola, New York. ISBN 9780486809038.
External links
- Essentially surjective functor at the nLab
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Functor types
- Additive
- Adjoint
- Conservative
- Derived
- Diagonal
- Enriched
- Essentially surjective
- Exact
- Forgetful
- Full and faithful
- Logical
- Monoidal
- Representable
- Smooth
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