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Extriangulated ideal quotients and Gabriel-Zisman localizations

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成果类型:
期刊论文
作者:
Liu, Yu;Zhou, Panyue
通讯作者:
Zhou, PY
作者机构:
[Liu, Yu] Shaanxi Normal Univ, Sch Math & Stat, Xian 710062, Peoples R China.
[Zhou, Panyue] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
通讯机构:
[Zhou, PY ] C
Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
语种:
英文
关键词:
cotorsion pairs;extriangulated categories;localizations;quotient categories
期刊:
中国科学:数学英文版
ISSN:
1674-7283
年:
2025
卷:
68
期:
3
页码:
507-532
基金类别:
National Natural Science Foundation of China [12171397, 12371034]; Hunan Provincial Natural Science Foundation of China [2023JJ30008]
机构署名:
本校为通讯机构
院系归属:
数学与统计学院
摘要:
Let $$(\cal{B},\mathbb{E},\mathfrak{s})$$ be an extriangulated category and $$\cal{S}$$ be an extension closed subcategory of ℬ. In this article, we prove that the Gabriel-Zisman localization $$\cal{B}/\cal{S}$$ can be realized as an ideal quotient inside ℬ when $$\cal{S}$$ satisfies some mild conditions. The ideal quotient is an extriangulated category. We show that the equivalence between the ideal quotient and the localization preserves the extriangulated category structure. We also discuss the r...

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