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

• Template:Nlab

1. REDIRECT Template:Category theory

• From a merge: This is a redirect from a page that was merged into another page. This redirect was kept in order to preserve the edit history of this page after its content was merged into the content of the target page. Please do not remove the tag that generates this text (unless the need to recreate content on this page has been demonstrated) or delete this page.
  • For redirects with substantive page histories that did not result from page merges use Template:Tl instead.

Template:Asbox