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...

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...

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...

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...

Antisymmetric tensor - Wikipedia, the free encyclopedia Antisymmetric tensor From Wikipedia, the free encyclopedia Jump to: navigation , search In ...

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

In differential geometry and general relativity , the Bach tensor is a tensor of rank 2 which is conformally invariant . In abstract indices the Ba...

The distinction is particularly important for computations with tensors , which often have mixed variance (both covariant and contravariant compone...

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...