Localization of extriangulated categories
Localization of extriangulated categories
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DOI：
10.1016/j.jalgebra.2022.08.008
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发表时间：
2021-03
影响因子：
0.9
通讯作者：
H. Nakaoka;Yasuaki Ogawa;Arashi Sakai
中科院分区：
文献类型：
--
作者：
H. Nakaoka;Yasuaki Ogawa;Arashi Sakai
在本文中，我们证明了满足温和假设的乘法系统对外三角范畴的定位可以配备自然的、通用的外三角范畴结构。这种构造统一了阿贝尔范畴的 Serre 商和三角范畴的 Verdier 商。事实上，我们为更广泛的态射类别提供了这样的构造，因此它涵盖了文献中出现的其他几个本地化，例如 Rump 通过双解析子类别对精确类别的本地化，通过 Hovey 孪生扭曲对对外三角类别的本地化，以及通过两侧可接纳渗透子类别对精确类别的本地化。
In this article, we show that the localization of an extriangulated category by a multiplicative system satisfying mild assumptions can be equipped with a natural, universal structure of an extriangulated category. This construction unifies the Serre quotient of abelian categories and the Verdier quotient of triangulated categories. Indeed we give such a construction for a bit wider class of morphisms, so that it covers several other localizations appeared in the literature, such as Rump's localization of exact categories by biresolving subcategories, localizations of extriangulated categories by means of Hovey twin cotorsion pairs, and the localization of exact categories by two-sided admissibly percolating subcategories.