Hearts of twin cotorsion pairs on exact categories
Hearts of twin cotorsion pairs on exact categories
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DOI：
10.1016/j.jalgebra.2013.07.028
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发表时间：
2013-02
期刊：
影响因子：
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通讯作者：
Y. Liu
中科院分区：
文献类型：
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作者：
Y. Liu
在论文中的Nakaoka，他介绍了心脏的概念（双）cotorsion对的三角范畴，并表明，他们有结构的（半）交换范畴。本文研究了具有足够投射和内射的正合范畴B上的孪生余扭对（S，T），（U，V），并引入了心的概念.首先，我们证明它的心是前阿贝尔的。此外，我们还证明了余挠对的心是阿贝尔的。这些结果与Nakaoka等人在三角范畴中的结果相似。我们还考虑了心脏结构更好的特殊情况。根据我们的结果，一个特殊的孪生余挠对（S，T），（T，V）的心是积分的，几乎是交换的。最后，我们证明了心在正则态射类上的Gabriel-Zisman局部化是阿贝尔的，并且它等价于B的稳定子范畴上的可表示模范畴.
In the papers of Nakaoka, he introduced the notion of hearts of (twin) cotorsion pairs on triangulated categories and showed that they have structures of (semi-) abelian categories. We study in this article a twin cotorsion pair (S, T),(U, V) on an exact category B with enough projectives 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 Nakaokaʼs results in triangulated categories. We also consider special cases where the heart has nicer structure. By our results, the heart of a special twin cotorsion pair (S, T),(T, V), is integral and almost abelian. Finally we show that the Gabriel–Zisman localization of the heart at the class of regular morphisms is abelian, and moreover it is equivalent to the category of finitely presented modules over a stable subcategory of B.