  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).
