# Essentially surjective functor

Jump to: navigation, search
${\displaystyle F:C\to D}$

is essentially surjective (or dense) if each object ${\displaystyle d}$ of ${\displaystyle D}$ is isomorphic to an object of the form ${\displaystyle Fc}$ for some object ${\displaystyle c}$ of ${\displaystyle C}$. Any functor which is part of an equivalence is essentially surjective.