… and injectives and introduce a notion of the heart. First we show that its heart is preabelian.
Moreover we show the heart of a single cotorsion pair is abelian. These results are analog of …

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

… , which is a generalization of the heart of a t-structure, has been proven to be abelian on …
hand, the heart of a twin cotorsion pair is not always abelian (it is only semi-abelian). In this …

… assumptions for the heart of a twin cotorsion pair to be integral and quasi-abelian. And in §5,
… the heart of a cotorsion pair ( S , T ) to a localization of the heart of a twin cotorsion pair of …

… -abelian. In this article, we consider a special class of hearts of twin cotorsion pairs induced
… We give a necessary and sufficient condition for such hearts to be abelian. In particular, we …

… The definition of the heart and its basic … heart of a twin cotorsion pair is always semi-abelian
(Theorem 2.32). Since we regard a cotorsion pair as a special case of a twin cotorsion pair (…

… category which is both left semi-abelian and right semi-abelian. A preabelian category A is
left … 2.5 to the case of pairs of cotorsion pairs. We work on a pair of cotorsion pairs (S,T ), (U,V) …

… cotorsion pairs and prove some lemmas which will be used later. In Section 3, we study a
localization of the heart of a cotorsion pair … It is semi-abelian by [12, Theorem 2.32]. In particular…

… condition for the heart of a twin cotorsion pair being abelian. Then by using the results we
have got, we investigate the almost split sequences in the hearts of twin cotorsion pairs. Finally…

… on exact categories”, we introduced the notion of the heart for any cotorsion pair on an exact
… ], we define hearts of cotorsion pairs on exact categories and proved that they are abelian. It …