A functorial approach to categorical resolutions

TL;DR

This paper introduces a functorial method using Auslander's formula to demonstrate that all Artin algebras have categorical resolutions, linking their derived categories and expanding understanding in representation theory.

Contribution

It provides a functorial approach to categorical resolutions of derived categories for Artin algebras, connecting finite global dimension cases to all Artin algebras.

Findings

Derived categories of finite global dimension Artin algebras determine those of all Artin algebras.

A functorial approach via Auslander's formula is effective for categorical resolutions.

The work applies functor categories to problems in representation theory.

Abstract

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, to categorical resolutions.