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...

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...

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

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...

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...

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

A bimorphism is a morphism that is both an epimorphism and a monomorphism. Isomorphism : f  : X ? Y is called an isomorphism if there exists a morp...

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

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...

Topology and Groupoids referenced below to obtain the fundamental groupoid of the orbit space of a discontinuous action of discrete group on a Haus...