Localization of triangulated categories with respect to extension-closed subcategories
Localization of triangulated categories with respect to extension-closed subcategories
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DOI：
10.1007/s10468-024-10272-y
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发表时间：
2024-05
影响因子：
0.6
通讯作者：
Yasuaki Ogawa
中科院分区：
文献类型：
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作者：
Yasuaki Ogawa
本文的目的是为三角范畴的本地化理论建立一个框架，即从给定的扩张闭子范畴出发，构造一个自然的外三角结构和一个满足适当普适性的精确函数，它统一了几个现象。准确地说，当且仅当本地化对应于三角范畴时，给定子范畴是粗的。在这种情况下，Q值只不过是通常的Verdier商。此外，还揭示了它是一个精确范畴当且仅当满足一个生成条件。这样的(阿贝尔)精确定域化提供了对某些上同调函子的很好的理解，例如，簇倾斜子范畴的心结构和阿贝尔商。
The aim of this paper is to develop a framework for localization theory of triangulated categories, that is, from a given extension-closed subcategoryof, we construct a natural extriangulated structure ontogether with an exact functorsatisfying a suitable universality, which unifies several phenomena. Precisely, a given subcategoryis thick if and only if the localizationcorresponds to a triangulated category. In this case,Qis nothing other than the usual Verdier quotient. Furthermore, it is revealed thatis an exact category if and only ifsatisfies a generating condition. Such an (abelian) exact localizationprovides a good understanding of some cohomological functors, e.g., the heart oft-structures onand the abelian quotient ofby a cluster-tilting subcategory.