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

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...

It follows that any functor which preserves limits will take terminal objects to terminal objects, and any functor which preserves colimits will ta...

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...

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

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...

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...

Similarly, the requirement for the ring multiplication to be associative is sometimes dropped, and rings in which the associative law holds are the...

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

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

In abstract algebra , a free algebra is the noncommutative analogue of a polynomial ring (which may be regarded as a free commutative algebra ). Le...