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...

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

C ) can be made precise in several ways; the most succinct formulation uses the language of adjoint functors . Every functor F  : D ? E induces a f...

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

Left derived functors are zero on all projective objects. One may also start with a contravariant left-exact functor F ; the resulting right-derive...

Spectral sequence Abelian category Triangulated category Derived category [ edit ] Applications Group cohomology Galois cohomology Lie algebra coho...

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

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...

Snake lemma - Wikipedia, the free encyclopedia Snake lemma From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematics , part...

For any appropriate maps g , h such that , then g = h . Suppose and in C . Then g and h are A -valued points of B , and therefore monomorphism is e...

Borel and Francesco Paolo Cantelli . Let ( E n ) be a sequence of events in some probability space . The Borel-Cantelli lemma states: If the sum of...

Commutativity makes sense for a polygon of any finite number of sides (including just 1 or 2), and a diagram is commutative if every polygonal subd...