A functorial approach to categorical resolutions

摘要

Using a relative version of Auslander’s formula,we give a functorial approach to show that the bounded derived category of every Artin algebra admits a categorical resolution.This,in particular,implies that the bounded derived categories of Artin algebras of finite global dimension determine bounded derived categories of all Artin algebras.Hence,this paper can be considered as a typical application of functor categories,introduced in representation theory by Auslander(1971),to categorical resolutions.