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

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 …

In the paper, we show that a uniformly bounded and nonnegative triangle functor between
Gorenstein derived categories of two CM-algebras induces a Gorenstein-projectively stable …

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 …

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 …

The aim of this paper is to introduce Gorenstein singularity category D gpsgb (A), as the
Verdier quotient of the Gorenstein derived category D gpb (A) by the triangulated …

Gorenstein derived categories are defined, and the relation with the usual derived
categories is given. The bounded Gorenstein derived categories of Gorenstein rings and of …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …

We prove a generalization of the stability for Gorenstein categories in [36] and [24]; and
show that the relative Auslander algebra of a CM-finite algebra is CM-free. On the other …

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 …