Triangulated Quotient Categories
Triangulated Quotient Categories
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DOI：
10.1080/00927872.2012.676116
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发表时间：
2012-04
影响因子：
0.7
通讯作者：
Y. Liu;Bin Zhu
中科院分区：
文献类型：
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作者：
Y. Liu;Bin Zhu
本文定义了右三角范畴中子范畴的变异概念。当（，）是右三角化范畴中的-突变对时，商范畴/自然带有右三角化结构。𝒵𝒵𝒟𝒞𝒵𝒟此外，如果右三角化范畴满足某些合理的条件，则右三角化商范畴/成为三角化范畴。𝒵𝒟当商是三角范畴时，我们的结果统一了Iyama-Yoshino和Jørgensen的商三角范畴的构造。𝒞
A notion of mutation of subcategories in a right triangulated category is defined in this article. When (𝒵, 𝒵) is a 𝒟-mutation pair in a right triangulated category 𝒞, the quotient category 𝒵/𝒟 carries naturally a right triangulated structure. Moreover, if the right triangulated category satisfies some reasonable conditions, then the right triangulated quotient category 𝒵/𝒟 becomes a triangulated category. When 𝒞 is triangulated, our result unifies the constructions of the quotient triangulated categories by Iyama-Yoshino and by Jørgensen, respectively.