Auslander--Iyama correspondence for exact dg categories

TL;DR

This paper extends the Auslander--Iyama correspondence to exact dg categories, generalizing known results for exact categories and providing a broader framework for higher Auslander theory.

Contribution

It introduces a generalization of the Auslander--Iyama correspondence to the setting of exact dg categories, broadening the scope of higher Auslander theory.

Findings

Extended Auslander--Iyama correspondence to exact dg categories.

Specialized to degree zero, recovered a generalization of higher Auslander correspondence.

Bridged the gap between dg categories and classical exact categories.

Abstract

We extend Auslander--Iyama correspondence to the setting of exact dg categories. By specializing it to exact dg categories concentrated in degree zero, we obtain a generalization of the higher Auslander correspondence for exact categories due to Ebrahimi--Nasr-Isfahani (in the case of exact categories with split retractions).