The heart of a cotorsion pair, which is a generalization of the heart of a t-structure, has been proven to be abelian on triangulated, exact, and extriangulated categories. On the other hand, the heart of a twin cotorsion pair is not always abelian (it is only semi-abelian). In this article, we study a special kind of hearts of twin cotorsion pairs induced by d -cluster tilting subcategories. We will give a sufficient-necessary condition when such hearts become abelian. We will also see that such hearts are hereditary.

中文翻译：

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双胞胎对的阿贝尔心

cotorsion pair 的中心是 t 结构中心的推广，已被证明在三角、精确和外三角范畴上是阿贝尔的。另一方面，双侧扭转对的心脏并不总是阿贝尔（它只是半阿贝尔）。在这篇文章中，我们研究了一种特殊的由 d 簇倾斜子类别引起的双扭转对的心。当这样的心变为阿贝尔心时，我们将给出充要条件。我们还将看到这样的心是遗传的。