Auslander's formula: Variations and applications

Abstract

According to Auslander's formula, one way of studying an abelian category C is to study mod-C, which has nicer homological properties than C, and then translate the results back to C. Recently, Krause gave a derived version of this formula and thus renewed the subject. This paper contains a detailed study of various versions of Auslander's formula, including the versions for all modules and for unbounded derived categories. We also include some results concerning recollements of triangulated categories. © 2020 by Kyoto University.