# Derived Functors

### Some articles on functor, derived functors, functors, derived:

Étale Cohomology - Definitions
... A presheaf on a topological space X is a contravariant functor from the category of open subsets to sets ... presheaf on a scheme X to be a contravariant functor from Et(X) to sets ... of sheaves of abelian groups over a scheme has enough injective objects, so one can define right derived functors of left exact functors ...
Sheaf (mathematics) - Sheaf Cohomology
... It was noted above that the functor preserves isomorphisms and monomorphisms, but not epimorphisms ... with values in an abelian category, then is actually a left exact functor ... This means that it is possible to construct derived functors of ...
Delta-functor
... In homological algebra, a δ-functor between two abelian categories A and B is a collection of functors from A to B together with a collection of morphisms that satisfy properties generalising those of ... A universal δ-functor is a δ-functor satisfying a specific universal property related to extending morphisms beyond "degree 0" ... by Alexander Grothendieck in his famous "Tohoku" paper to provide an appropriate setting for derived functors ...
Resolution (algebra) - Acyclic Resolution
... in a resolution, but in the behavior of the resolution with respect to a given functor ... situations, the notion of acyclic resolutions is used given a left exact functor F A → B between two abelian categories, a resolution of an object M of A is called F-acyclic, if the derived functors RiF(En ... Dually, a left resolution is acyclic with respect to a right exact functor if its derived functors vanish on the objects of the resolution ...
Derived Category - The Relation To Derived Functors
... The derived category is a natural framework to define and study derived functors ... In the following, let be a functor of abelian categories ... There are two dual concepts right derived functors are "deriving" left exact functors and are calculated via injective resolutions left derived functors come from right exact functors ...

### Famous quotes containing the word derived:

These are our grievances which we have thus laid before his majesty with that freedom of language and sentiment which becomes a free people, claiming their rights as derived from the laws of nature, and not as the gift of their chief magistrate.
Thomas Jefferson (1743–1826)