C ) can be made precise in several ways; the most succinct formulation uses the language of adjoint functors . Every functor F  : D ? E induces a f...

Problems formulated with adjoint functors 1.3 Adjoint functors as solving optimization problems 1.4 The case of partial orders 2 Formal definitions...

contravariant functor is right exact if and only if it turns finite limits into colimits. A functor is exact if and only if it is both left exact a...

C . (Recall that a category C is preadditive if all its morphism sets are Abelian groups and morphism composition is bilinear , i.e. if C is enrich...

As mentioned above, the category of all abelian groups is an abelian category. The category of all finitely generated abelian groups is also an abe...

Left derived functors are zero on all projective objects. One may also start with a contravariant left-exact functor F ; the resulting right-derive...

Category of vector spaces - Wikipedia, the free encyclopedia Category of vector spaces From Wikipedia, the free encyclopedia Jump to: navigation , ...

R -Mod, an injective object is an injective module . R -Mod has injective hulls (as a consequence, R-Mod has enough injectives). In the category of...

The functor category of all additive functors from this category to the category of abelian groups is isomorphic to the category of left modules ov...

Ext functor - Wikipedia, the free encyclopedia Ext functor From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematics , the ...

In that case, homotopy defines an equivalence relation on the hom sets in the model category giving rise to homotopy classes. [ edit ] Characteriza...

The dual concept to that of kernel is that of cokernel . That is, the kernel of a morphism is its cokernel in the opposite category , and vice vers...