Essentially surjective functor

In mathematics, specifically in category theory, a functor

${\displaystyle F:C\to D}$

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 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.^[1]

Notes[]

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

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