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...

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...

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

Subcategory Faithful functor Full functor Forgetful functor Yoneda lemma Representable functor Functor category Adjoint functors Galois connection ...

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...

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...

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...

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

It follows that any functor which preserves limits will take terminal objects to terminal objects, and any functor which preserves colimits will ta...

T 0 spaces is T 0 Every product of T 1 spaces is T 1 Every product of Hausdorff spaces is Hausdorff [1] Every product of regular spaces is regular ...