Let (C, E, s) be an extriangulated category. We show that certain quotient categories of
extriangulated categories are equivalent to module categories by some restriction of functor …

The concept of*-module arose from a remarkable converse of the tilting theorem due to
Menini and Orsatti [25] who essentially proved that for suitable full subcategories G & R-Mod …

Assume that $\mathcal {D} $ is a Krull-Schmidt, Hom-finite triangulated category with a Serre
functor and a cluster-tilting object $ T $. We introduce the notion of relative cluster tilting …

Abstract We consider a Krull–Schmidt, Hom-finite, 2-Calabi–Yau triangulated category with
a basic rigid object T, and show a bijection between the set of isomorphism classes of basic …

Let T be a Krull–Schmidt, Hom-finite triangulated category with suspension functor [1]. Let R
be a basic rigid object, Γ the endomorphism algebra of R, and pr (R)⊆ T the subcategory of …

We introduce the notion of homological systems Θ for triangulated categories. Homological
systems generalize, on one hand, the notion of stratifying systems in module categories, and …

For a recollement ( A , B , C ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}
\usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} …

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We prove that certain subquotient categories of extriangulated categories are abelian. As a
particular case, if an extriangulated category CC has a cluster-tilting subcategory XX, then …

Tilting modules arose from representation theory of algebras and are known to furnish
equivalences between categories of modules. We single out some weaker properties which …