Given an abelian category, the filtered derived category is the category of chain complexes of filtered objects up to quasi-isomorphism.
Given an abelian category , one may consider the additive category of filtered objects in , whose objects are pairs with an object of and a filtration on . Let denote the category of chain complexes in . One defines a morphism in to be a quasi-isomorphism if it induces quasi-isomorphisms on each degree of the associated graded objects. The filtered derived category of ,
is the localization of at the class of quasi-isomorphisms.
Created on October 27, 2014 at 15:39:27. See the history of this page for a list of all contributions to it.