The Right Gorenstein Subcategory rG(C,D).

In this paper, we generalize the idea of Song, Zhao and Huang [Czechoslov. Math. J., 70, 483–504 (2020)] and introduce the notion of right (left) Gorenstein subcategory r G (C , D) (l G (C , D)) , relative to two additive full subcategories C and D of an abelian category A . Under the assumption that C ⊆ D , we prove that the right Gorenstein subcategory r G (C , D) possesses many nice properties that it is closed under extensions, kernels of epimorphisms and direct summands. When C ⊆ D and C ⊥ D , we show that the right Gorenstein subcategory r G (C , D) admits some kind of stability. Then we discuss a resolution dimension for an object in A , called r G (C , D) -projective dimension. Finally, we prove that if (U , V) is a hereditary cotorsion pair with kernel C has enough injectives, such that U ⊆ D and U ⊥ D , then (r G (C , D) , r e s C ^ , C) is a weak Auslander—Buchweitz context, where res C ^ is the subcategory of A consisting of objects with finite C -projective dimension. [ABSTRACT FROM AUTHOR]