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...

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...

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

P. Freyd [1] ) if it contains all the objects of C . A lluf subcategory is typically not full: the only full lluf subcategory of a category is that...

R -Mod, an injective object is an injective module . R -Mod has injective hulls (as a consequence, R-Mod has enough injectives). In the category of...

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

Ext functor - Wikipedia, the free encyclopedia Ext functor From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematics , the ...

Then we obtain a commutative diagram in which all the diagonals are short exact sequences: Conversely, given any list of overlapping short exact se...

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

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

In general, arbitrary direct sums and direct limits of flat modules are flat, a consequence of the fact that the tensor product commutes with direc...