Let 𝒜 be an abelian category. A subcategory 𝒳 of 𝒜 is called coresolving if 𝒳 is closed under
extensions and cokernels of monomorphisms and contains all injective objects of 𝒜. In this …

Let 𝒜 be an abelian category and 𝒳, 𝒴, 𝒵 additive full subcategories of 𝒜. We introduce and
study the Gorenstein category 𝒢 (𝒳, 𝒴, 𝒵) as a common generalization of some known …

Let $\mathcal {C} $ be a triangulated category with a proper class $\xi $ of triangles.
Asadollahi and Salarian introduced and studied $\xi $-Gorenstein projective and $\xi …

Let ℰ be an injectively resolving subcategory of left R-modules. We introduce and study ℰ-
Gorenstein flat modules as a common generalization of some known modules such as …

Relations between Gorenstein derived categories, Gorenstein defect categories and
Gorenstein stable categories are established. Using these, the Gorensteinness of an …

Let G (X) and G (Y) be Gorenstein subcategories induced by an admissible balanced pair
(X, Y) in an abelian category A. In this paper, we establish Gorenstein homological …

Let A be an abelian category and P (A) be the subcategory of A consisting of projective
objects. Let C be a full, additive and self-orthogonal subcategory of A with P (A) a generator …

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 …

We introduce compatible bimodules. If M is a compatible A–B-bimodule, then the Gorenstein-
projective modules over algebra Λ=(AM0B) are explicitly described; and if Λ is Gorenstein …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact …