Extriangulated ideal quotients and Gabriel-Zisman localizations  

作　　者：Yu Liu Panyue Zhou 

机构地区：[1]School of Mathematics and Statistics,Shaanxi Normal University,Xi’an,710062,China [2]School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha,410114,China

出　　处：《Science China Mathematics》2025年第3期507-532,共26页中国科学(数学英文版)

基　　金：supported by National Natural Science Foundation of China(Grant No.12171397);Panyue Zhou was supported by National Natural Science Foundation of China(Grant No.12371034);the Hunan Provincial Natural Science Foundation of China(Grant No.2023JJ30008)。

摘　　要：Let(B,E,s)be an extriangulated category and S be an extension closed subcategory of B.In this article,we prove that the Gabriel-Zisman localization B/S can be realized as an ideal quotient inside B when 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 relations of our results with Hovey twin cotorsion pairs and Verdier quotients.

关 键 词：cotorsion pairs extriangulated categories LOCALIZATIONS quotient categories 

分 类 号：O154.1[理学—数学]