Let $\mathscr{ C}$ be an additive subcategory of left $\Lambda$-modules, we establish relations of the orthogonal classes of $\mathscr{ C}$ and (co)res $\widetilde{ \mathscr{ C}}$ 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.
Categories: math.RT math.AC