Essentially surjective functor

In mathematics, specifically in category theory, a functor

$F:C\to D$

is essentially surjective 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.

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