We give a simultaneous generalization of exact categories and triangulated categories,
which is suitable for considering cotorsion pairs, and which we call extriangulated …

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 …

Abstract Quillen's Resolution Theorem in algebraic K-theory provides a powerful
computational tool for calculating K-groups of exact categories. At the level of K 0, this result …

We generalise some of the theory developed for abelian categories in papers of Auslander
and Reiten to semi-abelian and quasi-abelian categories. In addition, we generalise some …

Nakaoka and Palu introduced the notion of extriangulated categories by extracting the
similarities between exact categories and triangulated categories. In this paper, we study …

We give a simultaneous generalization of exact categories and triangulated categories,
which is suitable for considering cotorsion pairs, and which we call extriangulated …

In the papers of Nakaoka, he introduced the notion of hearts of (twin) cotorsion pairs on
triangulated categories and showed that they have structures of (semi-) abelian categories …

It was shown recently that the heart H¯ of a twin cotorsion pair ((S, T),(U, V)) on an
extriangulated category is semi-abelian. We provide a sufficient condition for the heart to be …

Integral categories form a sub-class of pre-abelian categories whose systematic study was
initiated by Rump in 2001. In the first part of this article we determine whether several …

The aim of this paper is to develop a framework for localization theory of triangulated
categories\(\mathcal {C}\), that is, from a given extension-closed subcategory\(\mathcal {N}\) …