Based on Beligiannis's theory in [Beligiannis, A.(2000). Relative homological algebra and
purity in triangulated categories. J. Algebra 227 (1): 268–361], we introduce and study E …

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) …

In this article, we study the heart of a cotorsion pairs on an exact category and a triangulated
category in a unified method, by means of the notion of an extriangulated category. We …

Let T be a triangulated category with a proper class ξ of triangles. We introduce the notions
of left Frobenius pairs, left (n-) cotorsion pairs and left (weak) Auslander-Buchweitz contexts …

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 …

Let $\mathscr {C} $ be an extriangulated category with enough projectives and injectives.
We give a new definition of tilting subcategories of $\mathscr {C} $ and prove it coincides …

We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …

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 …

In the present article, we study the relationship of cotorsion pairs among three triangulated
categories in a recollement. We show that if a triangulated category 𝒟 admits a recollement …

Assume that D is a Krull-Schmidt, Hom-finite triangulated category with a Serre functor and a
cluster-tilting object T. We introduce the notion of ghost-tilting objects, and T [1]-tilting objects …