Extriangulated categories were introduced by Nakaoka and Palu to give a unification of properties in exact categories and extension-closed subcategories of triangulated categories. A notion of tilting pairs in an extriangulated category is introduced in this paper. We give a Bazzoni characterization of tilting pairs in this setting. We also obtain the Auslander–Reiten correspondence of tilting pairs which classifies finite $\mathcal {C}$-tilting subcategories for a certain self-orthogonal subcategory $\mathcal {C}$ with some assumptions. This generalizes the known results given by Wei and Xi for the categories of finitely generated modules over Artin algebras, thereby providing new insights in exact and triangulated categories.

Given a non-negative integer n and a complete hereditary cotorsion triple , the notion of subcategories in an abelian category is introduced. It is proved that a virtually Gorenstein ring R is n-Gorenstein if and only if the subcategory of Gorenstein injective R-modules is with respect to the cotorsion triple , where stands for the subcategory of Gorenstein projectives. In the case when a subcategory of is closed under direct summands such that each object in admits a right -approximation, a Bazzoni characterization is given for to be . Finally, an Auslander–Reiten correspondence is established between the class of subcategories and that of certain subcategories of which are -coresolving covariantly finite and closed under direct summands.