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 …

In the paper of Keller and Reiten, it was shown that the quotient of a triangulated category
(with some conditions) by a cluster tilting subcategory becomes an abelian category. After …

In the preceding part (I) of this paper, we showed that for any torsion pair (ie, t-structure
without the shift-closedness) in a triangulated category, there is an associated abelian …

We show that the relative Auslander–Buchweitz context on a triangulated category T
coincides with the notion of co-t-structure on certain triangulated subcategory of T (see …

A class of triangulated categories with a finiteness condition is singled out. These
triangulated categories have Auslander–Reiten triangles. It is proved that the relations of the …

In this article, we introduce the notion of concentric twin cotorsion pair on a triangulated
category. This notion contains the notions of t-structure, cluster tilting subcategory, co-t …

A notion of mutation of subcategories in a right triangulated category is defined in this article.
When (𝒵, 𝒵) is a 𝒟-mutation pair in a right triangulated category 𝒞, the quotient category 𝒵/𝒟 …

Extriangulated categories were introduced by Nakaoka and Palu to give a unification of
properties in exact categories and triangulated categories. We consider in this article the …

Right triangulated categories can be thought of as triangulated categories whose shift
functor is not an equivalence. We give intrinsic characterisations of when such categories …

Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …