构造三角模型结构的新方法

doi:10.6040/j.issn.1671-9352.0.2020.194

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (12): 97-102.doi: 10.6040/j.issn.1671-9352.0.2020.194

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构造三角模型结构的新方法

张平儿,杨晓燕

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2020-12-01
作者简介:张平儿(1993— ), 男, 硕士研究生, 研究方向为同调代数. E-mail:275661482@qq.com
基金资助:
国家自然科学基金资助项目(11761060)

A new construction method of triangulated model structures

ZHANG Ping-er, YANG Xiao-yan

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2020-12-01

摘要/Abstract

摘要： 设T 是三角范畴,ξ表示某个三角真类。假设(Q,R)和(Q,R)是两个相对于ξ的完备遗传余挠对,其中R⊆R且Q ∩R=Q∩R。在T 中构造了一个相对于ξ的唯一三角模型结构,Q(Q)作为余纤维(平凡的余纤维)对象的类,R(R)作为纤维(平凡的纤维)对象的类。

关键词: 三角范畴, 完备遗传余挠对, thick类, Hovey三元组

Abstract: Let T be a triangulated category and ξ denote some proper class of triangles, and suppose that we have two complete hereditary cotorsion pairs(Q,R)and(Q,R)with respect to ξ in T satisfying R⊆R and Q ∩R=Q∩R. We show how to construct an unique triangulated model structures with respect to ξ on T with Q(resp.Q)as the class of cofibrant(resp. trivially cofibrant)objects and R(resp. R)as the class of fibrant(resp. trivially fibrant)objects.

Key words: triangulated category, complete hereditary cotorsion pair, thick class, Hovey triple

中图分类号:

O154.2

张平儿,杨晓燕. 构造三角模型结构的新方法[J]. 《山东大学学报(理学版)》, 2020, 55(12): 97-102.

ZHANG Ping-er, YANG Xiao-yan. A new construction method of triangulated model structures[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 97-102.

参考文献

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构造三角模型结构的新方法

A new construction method of triangulated model structures

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