Gorenstein categories and separable equivalences

Abstract

Let $\mathcal{C}$ be an additive subcategory of left $\hat{I}›$-modules, we establish relations of the orthogonal classes of $\mathcal{C}$ and (co)res $\tilde{\mathcal{C}}$ under separable equivalences. As applications, we obtain that the (one-sided) Gorenstein category and Wakamatsu tilting module are preserved under separable equivalences. Furthermore, we discuss when $G_C$-projective (injective) modules and Auslander (Bass) class with respect to $C$ are invariant under separable equivalences.

12 pages