Balanced pairs appear naturally in the realm of relative homological algebra associated with the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural source of such pairs. In this paper, we study the connection between balanced pairs and cotorsion triplets by using recent quiver representation techniques. In doing so, we find a new characterization of abelian categories that have enough projectives and injectives in terms of the existence of complete hereditary cotorsion triplets. We also provide a short proof of the lack of balance for derived functors of Hom computed using flat resolutions, which extends the one given by Enochs in the commutative case.

中文翻译：

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平衡对、cotorsion 三元组和颤动表示

平衡对自然出现在与右派生函子的平衡相关的相对同调代数领域中霍姆函子。Cotorsion 三元组是这种对的自然来源。在本文中，我们使用最近的箭袋表示技术研究了平衡对和 cotorsion 三元组之间的联系。在这样做的过程中，我们发现了一个新的阿贝尔范畴的表征，该范畴具有足够的射影和射影，就存在完整的遗传 cotorsion 三元组而言。我们还提供了一个关于派生函子缺乏平衡的简短证明霍姆使用平面分辨率计算，它扩展了在交换情况下由 Enochs 给出的分辨率。