Yoneda's lemma asserts that every natural transformation between Hom functors is of this form. In other words, the Hom functors give rise to a full...

Diagonal functor : The diagonal functor is defined as the functor from D to the functor category D C which sends each object in D to the constant f...

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...

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

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...

If there is a monoidal functor from a monoidal category M to a monoidal category N , then any category enriched over M can be reinterpreted as a ca...

Indeed, the term "zero object" originated in the study of preadditive categories like Ab , where the zero object is the zero group . A preadditive ...

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...

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...

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

P. Freyd [1] ) if it contains all the objects of C . A lluf subcategory is typically not full: the only full lluf subcategory of a category is that...

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