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...

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...

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...

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...

Set (with the monoidal structure induced by the cartesian product) is a monoid in the usual sense. A monoid object in Top (with the monoidal struct...

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

It follows that if coproducts exists in a given category (they need not) they are unique up to a unique isomorphism that respects the injections. I...

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

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

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...

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...

This is a glossary of tensor theory . For expositions of tensor theory from different points of view, see: Tensor Classical treatment of tensors Te...