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 …

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 this paper, we introduce and study relative phantom morphisms in extriangulated
categories defined by Nakaoka and Palu. Then using their properties, we show that if (𝒞, 𝔼 …

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 …

Abstract Let (C, E, s) be an Ext-finite, Krull-Schmidt and k-linear extriangulated category with
ka commutative artinian ring. We define an additive subcategory C r (respectively, C l) of C …

The hearts of cotorsion pairs on extriangulated categories are abelian categories. On the
other hand, the hearts of twin cotorsion pairs are not always abelian. They were shown to be …

We prove that, under a mild assumption, the heart H‾ of a twin cotorsion pair ((S, T),(U, V))
on a triangulated category C is a quasi-abelian category. If C is also Krull-Schmidt and T= U …