Preservation of limits Representable functors are naturally isomorphic to Hom functors and therefore share their properties. In particular, (covari...

Functors Main article: functor Functors are structure-preserving maps between categories. They can be thought of as morphisms in the category of al...

Ab is injective if and only if it is divisible ; it is projective if and only if it is a free abelian group. The category has a projective generato...

A bimorphism is a morphism that is both an epimorphism and a monomorphism. Isomorphism : f  : X ? Y is called an isomorphism if there exists a morp...

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

In the various branches of mathematics that fall under the heading of abstract algebra , the kernel of a homomorphism measures the degree to which ...

In that case, homotopy defines an equivalence relation on the hom sets in the model category giving rise to homotopy classes. [ edit ] Characteriza...

Accidental isomorphisms 2 Indefinite signature 3 Topological considerations 4 See also [ edit ] Accidental isomorphisms In low dimensions, there ar...

Short five lemma - Wikipedia, the free encyclopedia Short five lemma From Wikipedia, the free encyclopedia Jump to: navigation , search In mathemat...