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...

If there is a monoidal functor from a monoidal category M to a monoidal category N , then any category enriched over M can be reinterpreted as a ca...

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...

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 ...

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...

Another article treats the concept of species in biology . In combinatorial mathematics , the theory of combinatorial species is an abstract, syste...

See finite morphism . The morphism f is locally of finite type if Y may be covered by affine open sets Spec B such that each inverse image f ? 1 (S...

While all these conditions are equivalent for metric spaces , in general we have the following implications: Compact spaces are countably compact. ...

Alexandrov spaces can be viewed as a generalization of finite topological spaces . Contents 1 Characterizations of Alexandrov topologies 2 Duality ...

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...