Auslander’s formula: Variations and applications

Abstract

According to Auslander’s formula, one way of studying an abelian category $\mathcal{C}$ is to study $\mathrm{mod-}\mathcal{C}$, which has nicer homological properties than $\mathcal{C}$, and then translate the results back to $\mathcal{C}$. 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.