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 …

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 …

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 …

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 …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

In this article, we show that the localization of an extriangulated category by a multiplicative
system satisfying mild assumptions can be equipped with a natural, universal structure of an …

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 …

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 …