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

Let $ k $ be a commutative ring, let ${\mathcal {C}} $ be a small, $ k $-linear, Hom-finite,
locally bounded category, and let ${\mathcal {B}} $ be a $ k $-linear abelian category. We …

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 …

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 …

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

In this paper we construct Gorenstein-projective modules over Morita rings with zero
bimodule homomorphisms and we provide sufficient conditions for such rings to be …

We prove that if the Frobenius functor F (from the category of left R-modules to the category
of left S-modules) is faithful, then for any R-module X, the Gorenstein flat dimension of X is …

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 the notion of relative singularity category with respect to any self-orthogonal
subcategory $\omega $ of an abelian category. We introduce the Frobenius category of …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …