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 (Iyama–Solberg 2018) for exact categories. Our approach is based on the recent generalization of the (higher) Auslander correspondence to exact categories (Henrard–Kvamme–Roosmalen 2020, Ebrahimi–Nasr-Isfahani 2021).