Namely, we can demand the existence of a tensor product that is left adjoint to the internal Hom functor . In this approach, closed monoidal catego...

G -sets are nothing but functors from this category to Set The category of all directed graphs is cartesian closed; this is a functor category as e...

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...

The smash product of any pointed space X with a 0-sphere is homeomorphic to X . The smash product of two circles is a quotient of the torus homeomo...

Preservation of limits Representable functors are naturally isomorphic to Hom functors and therefore share their properties. In particular, (covari...

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...

Simplicial category - Wikipedia, the free encyclopedia Simplicial category From Wikipedia, the free encyclopedia Jump to: navigation , search In ma...

Functors Main article: functor Functors are structure-preserving maps between categories. They can be thought of as morphisms in the category of al...

Adjoint endomorphism - Wikipedia, the free encyclopedia Adjoint endomorphism From Wikipedia, the free encyclopedia Jump to: navigation , search In ...

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...

Ab is injective if and only if it is divisible ; it is projective if and only if it is a free abelian group. The category has a projective generato...