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 …

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 and study the notion of Gorenstein silting complexes, which is a generalization
of Gorenstein tilting modules in Gorenstein-derived categories. We give the equivalent …

Presilting and silting subcategories in extriangulated categories were introduced by Adachi
and Tsukamoto recently. In this paper, we prove that the Gabriel-Zisman localization …

Abstract Let \ mathscr {C\} C be a triangulated category and \ mathscr {X\} X be a cluster
tilting subcategory of \ mathscr {C\} C. Koenig and Zhu showed that the quotient category …

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 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 $\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 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 …

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. A notion of proper class in an …