• Source: Essentially surjective functor

In mathematics, specifically in category theory, a functor




F
:
C
→
D


{\displaystyle F:C\to D}


is essentially surjective if each object



d


{\displaystyle d}

of



D


{\displaystyle D}

is isomorphic to an object of the form



F
c


{\displaystyle Fc}

for some object



c


{\displaystyle c}

of



C


{\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.




Notes






References






External links


Essentially surjective functor at the nLab

Kata Kunci Pencarian:

• Essentially surjective functor
• Equivalence of categories
• Anafunctor
• Category of topological spaces
• Sheaf (mathematics)
• Triangulated category
• Category of measurable spaces
• Quotient of an abelian category
• Glossary of category theory
• Ind-completion