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...

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...

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...

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...

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

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

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...

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...

Transformation of local covariant basis in the case of general curvilinear coordinates As stated above, contravariant vectors are vectors with cont...

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

A vector space with a topology compatible with the operations — such that addition and scalar multiplication are continuous maps — is called a topo...

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...