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...

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...

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...

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...

Limits and universal morphisms Colimits in comma categories may be "inherited". If and are cocomplete, is a cocontinuous functor, and another funct...

Final topology - Wikipedia, the free encyclopedia Final topology From Wikipedia, the free encyclopedia Jump to: navigation , search In general topo...

Definition: Tensor Product of Vector Spaces 2 Alternate notation 3 Tensor fields 4 Basis [ edit ] Definition: Tensor Product of Vector Spaces Let V...

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

Given again the finite-dimensional case, if bases have been chosen, then the composition of linear maps corresponds to the matrix multiplication , ...