Motivated by the classical structure of Tate cohomology, we develop and study a Tate
cohomology theory in a triangulated category C. Let E be a proper class of triangles. By …

Let C be a triangulated category. We first introduce the notion of balanced pairs in C, and
then establish the bijective correspondence between balanced pairs and proper classes ξ …

In this paper, we study (complete) cotorsion pairs in extriangulated categories. First, we
study a relationship between an interval of the poset of cotorsion pairs and the poset of …

Let $\mathcal B $ be an extriangulated category with enough projectives and enough
injectives. We define a proper $ m $-term subcategory $\mathcal G $ on $\mathcal B …

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. In this paper, we show that …

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 …

Let X be a semibrick in an extriangulated category C. Let T be the filtration subcategory
generated by X. We give a one-to-one correspondence between simple semibricks and …

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

In this paper, the authors introduce a new definition of∞-tilting (resp. cotilting) subcategories
with infinite projective dimensions (resp. injective dimensions) in an extriangulated category …

In the previous article “Hearts of twin cotorsion pairs on exact categories. J. Algebra, 394,
245–284 (2013)”, we introduced the notion of the heart for any cotorsion pair on an exact …