Hearts of twin cotorsion pairs on extriangulated categories
Hearts of twin cotorsion pairs on extriangulated categories
复制标题
DOI：
10.1016/j.jalgebra.2019.03.005
复制
发表时间：
2017-02
影响因子：
0.9
通讯作者：
Y. Liu;H. Nakaoka
中科院分区：
文献类型：
--
作者：
Y. Liu;H. Nakaoka
本文利用外三角范畴的概念，用统一的方法研究了正合范畴和三角范畴上的余挠对的心。证明了心是阿贝尔的，并构造了心的上同调函子。如果外三角范畴有足够的射影，这个函子给出了心与余心模射影上的凝聚函子范畴之间的等价性。我们还证明了一个外三角范畴的一个ann-簇倾斜子范畴如何产生一族具有等价心的余挠对。
In this article, we study theheartof a cotorsion pairs on an exact category and a triangulated category in a unified method, by means of the notion of anextriangulated category. We prove that the heart is abelian, and construct a cohomological functor to the heart. If the extriangulated category has enough projectives, this functor gives an equivalence between the heart and the category of coherent functors over thecoheartmodulo projectives. We also show how ann-cluster tilting subcategoryof an extriangulated category gives rise to a family of cotorsion pairs with equivalent hearts.