Higher Auslander--Solberg correspondence for exact categories

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).