Essentially surjective functor

In mathematics, specifically in category theory, a functor

[math]\displaystyle{ F:C\to D }[/math]

is essentially surjective if each object [math]\displaystyle{ d }[/math] of [math]\displaystyle{ D }[/math] is isomorphic to an object of the form [math]\displaystyle{ Fc }[/math] for some object [math]\displaystyle{ c }[/math] of [math]\displaystyle{ C }[/math].

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. 

External links

• Essentially surjective functor in nLab