Extriangulated categories axiomatize extension-closed subcategories of triangulated
categories and generalise both exact categories and triangulated categories. This survey …

We show that the mesh mutations are the minimal relations among the gg‐vectors with
respect to any initial seed in any finite‐type cluster algebra. We then use this algebraic result …

We introduce the notion of an exact dg category, which is a simultaneous generalization of
the notions of exact category in the sense of Quillen and of pretriangulated dg category in …

We initiate the study of derived functors in the setting of extriangulated categories. By using
coends, we adapt Yoneda's theory of higher extensions to this framework. We show that …

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) …

We extend results of Br\" ustle-Yang on ideal quotients of 2-term subcategories of perfect
derived categories of non-positive dg algebras to a relative setting. We find a new …

In this article, we initiate the study of hereditary extriangulated categories. Many important
categories arising in representation theory in connection with various theories of mutation …

Examples of exact categories in representation theory are given by the category of Δ-filtered
modules over quasi-hereditary algebras, but also by various categories related to matrix …

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 …

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 …