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...

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...

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

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...

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...

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

As mentioned above, the category of all abelian groups is an abelian category. The category of all finitely generated abelian groups is also an abe...

Distinction with symmetric tensors The symmetric algebra and symmetric tensors are easily confused: the symmetric algebra is a quotient of the tens...

V  ' into a normed vector space. An important theorem about continuous linear functionals on normed vector spaces is the Hahn-Banach theorem . [ ed...

When an object is accelerated, the object's velocity vector changes per unit of time. Acceleration can change the direction of the velocity vector,...

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