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.Mac Lane (1998), Theorem IV.4.1

Notes

References

{{Cite book

|first=Saunders

|last=Mac Lane

|authorlink=Saunders Mac Lane

|title=Categories for the Working Mathematician

|edition=second

|date=September 1998

|publisher=Springer

|isbn=0-387-98403-8}}

{{cite book |isbn=9780486809038|url=https://math.jhu.edu/~eriehl/context/|title=Category Theory in Context |last1=Riehl |first1=Emily |year=2016|publisher=Dover Publications, Inc Mineola, New York}}

External links

{{nlab|id=essentially+surjective+functor|title=Essentially surjective functor}}

Category:Functors