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...

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

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

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...

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 ...

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

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...