Higher Auslander--Solberg correspondence for exact categories

TL;DR

This paper extends the higher Auslander--Solberg correspondence to exact categories by introducing new concepts like $n$-minimal Auslander--Gorenstein categories and $n$-precluster tilting subcategories, broadening the theoretical framework.

Contribution

It develops an analog of the higher Auslander--Solberg correspondence specifically for exact categories, building on recent generalizations of Auslander correspondence.

Findings

Introduces $n$-minimal Auslander--Gorenstein categories

Defines $n$-precluster tilting subcategories

Establishes the higher Auslander--Solberg correspondence for exact categories

Abstract

We introduce the concept of an $n$-minimal Auslander--Gorenstein category and $n$-precluster tilting subcategory. With this, we create an analog of the higher Auslander--Solberg correspondence (arXiv:1608.04179) for exact categories. Our approach is based on the recent generalization of the (higher) Auslander correspondence to exact categories (arXiv:2011.15107, arXiv:2108.13645).