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...

anafunctor. For example, the statement "every fully faithful and essentially surjective functor is an equivalence of categories" is equivalent to the axiom...

morphisms between them. Thus any functor from C {\displaystyle C} to E {\displaystyle E} will not be essentially surjective. Consider a category C {\displaystyle...

are functions preserving this structure. There is a natural forgetful functor U : Top → Set to the category of sets which assigns to each topological...

{G}}(U)} are not always surjective for epimorphisms of sheaves is equivalent to non-exactness of the global sections functor—or equivalently, to non-triviality...

category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category...

are the surjective measurable maps, and the isomorphisms are the isomorphisms of measurable spaces. The split monomorphisms are (essentially) the inclusions...

{B}}\cong {\mathcal {C}}} if and only if there exists an exact and essentially surjective functor F : A → C {\displaystyle F\colon {\mathcal {A}}\to {\mathcal...

if there is an equivalence between them. essentially surjective A functor F is called essentially surjective (or isomorphism-dense) if for every object...

1 ( y ) = { x } . {\displaystyle f^{-1}(y)=\{x\}.} The function f is surjective (or onto, or is a surjection) if its range f ( X ) {\displaystyle f(X)}...