… we study the heart of a cotorsion pairs on an exact category and a triangulated category in a
… that all these resulting cotorsion pairs have equivalent hearts, which are equivalent to some …

… heart H ‾ of a twin cotorsion pair ( ( S , T ) , ( U , V ) ) on a triangulated category C is a
quasi-abelian category. … show that the heart of the cotorsion pair ( S , T ) is equivalent to the …

… of the ambient triangulated category), … heart of a twin cotorsion pair to be integral and
quasi-abelian. And in §5, we show there is an explicit equivalence from the heart of a cotorsion pair …

… If one considers a cotorsion pair in a triangulated category, it becomes essentially the same
… Then the following statements are equivalent: (a) M is fully rigid; (b) C ≃ H/M; (c) C is abelian…

… the notion of cotorsion pairs in triangulated categories and … The heart of such twin cotorsion
pair is just \(\mathcal B/\mathcal T\)… , the localization of the heart is equivalent to the heart of \((\…

… hearts of twin cotorsion pairs. Finally, as an application, we show that a Krull-Schmidt,
Hom-finite triangulated category … to the regular morphisms on it is equivalent to mod EndC(T)op. …

… Hom-finite triangulated category is equivalent to the localization of the category with respect
to … a subcategory H ⊆ B, which we call the heart of the twin cotorsion pair [15, 16]. It is semi-…

… (S, T ), (U, V)) be a concentric twin cotorsion pair in an extriangulated … Note that this condition
is equivalent to S⊆U, and also to V⊆… Then H/I is the heart of the cotorsion pair (U, V). By [7, …

… article “Hearts of twin cotorsion pairs on exact categories. J. … sufficient condition when two
different hearts are equivalent. … sequences are introduced on triangulated categories, we will …

… heart H of a twin cotorsion pair ((S,T ),(U,V)) on a triangulated category C is a quasi-abelian
category… T = U, we show that the heart of the cotorsion pair (S,T ) is equivalent to the Gabriel-…