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...

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...

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...

Limits and universal morphisms Colimits in comma categories may be "inherited". If and are cocomplete, is a cocontinuous functor, and another funct...

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

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...

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 ...

Complete algebraic variety - Wikipedia, the free encyclopedia Complete algebraic variety From Wikipedia, the free encyclopedia   (Redirected from C...

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

For non first-countable spaces, sequential continuity might be strictly weaker than continuity. (The spaces for which the two properties are equiva...