Let XX be a resolving subcategory of an abelian category. In this paper we investigate the
singularity category D_ sg (X)= D^ b (mod\, X)/K^ b (proj (mod\, X)) D sg (X ̲)= D b (mod X …

We introduce the notion of relative singularity category with respect to a self‐orthogonal
subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen …

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 …

We study the properties of the relative derived category DC b (A) of an abelian category A
relative to a full and additive subcategory C. In particular, when A= A-mod for a finite …

We investigate the behavior of singularity categories and stable categories of Gorenstein
projective modules along a morphism of rings. The natural context to approach the problem …

We study singularity categories through Gorenstein objects in triangulated categories and
silting theory. Let ω be a presilting subcategory of a triangulated category T. We introduce …

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 …

We show the existence of a full exceptional collection in the graded stable derived category
of a Gorenstein isolated quotient singularity using a result of Orlov (2009)[Orl09]. We also …

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 …

Contravariantly finite resolving subcategories of the category of finitely generated modules
have been playing an important role in the representation theory of algebras. In this paper …