| 正合范畴中的复形、余挠对及粘合 |
| |
| 引用本文： | 郭寿桃,杨晓燕.正合范畴中的复形、余挠对及粘合[J].数学年刊A辑(中文版),2021,42(1):59-74. |
| |
| 作者姓名： | 郭寿桃 杨晓燕 |
| |
| 作者单位： | 西北师范大学数学与统计学院, 兰州~730070. |
| |
| 基金项目： | 国家自然科学基金~(No.\,11761060) |
| |
| 摘 要： | 作者在弱幂等完备的正合范畴(A,ε)中引入了复形的新的定义,并且证明了ε-正合复形的同伦范畴κex(ε)是同伦范畴κε(A)的厚子范畴.给定(A,ε)中的余挠对(x,y),定义了正合范畴(cε(A),C(ε))中的两个余挠对(x~ε,dgy~ε)和(dgx~ε,y~ε),并且证明了当A是可数完备时,cε(A)中任意无界复形的dgx~ε,y~ε-分解存在.作为应用,建立了相对于范畴κex(ε)和Dε(A)的范畴κ_ε(A)的左粘合,给出了R-模范畴的粘合的例子.
|
| 关 键 词： | 正合范畴 复形 余挠对 粘合 |
| 收稿时间： | 2019/5/17 0:00:00 |
| 修稿时间： | 2020/7/31 0:00:00 |
Complexes, Cotorsion Pairs and Recollements on Exact Categories |
| |
| GUO Shoutao,YANG Xiaoyan.Complexes, Cotorsion Pairs and Recollements on Exact Categories[J].Chinese Annals of Mathematics,2021,42(1):59-74. |
| |
| Authors: | GUO Shoutao YANG Xiaoyan |
| |
| Institution: | School of Mathematics and Statistics, Northwest Normal University,Lanzhou 730070, China.; Corresponding author. School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. |
| |
| Abstract: | In this paper, a new definition of complexes on a weakly idempotent complete exact category (A , E ) is introduced. The authors prove that the homotopy category Kex(E ) of E -exact complexes is a thick subcategory of the homotopy category KE (A ). Given a cotorsion pair (X , Y ) in (A , E ), they define two cotorsion pairs ( fXE , dg fYE ) and (dgXfE , YfE ) on the exact category (CE (A ), C(E )), and prove the existence of dg fXE -resolution for any unbounded complex in CE (A ) whenever A is countably complete. As an application of these results, the authors establish a left recollement of KE (A ) relative to Kex(E ) and DE (A ).Some examples of recollements on the category of R-modules are given. |
| |
| Keywords: | Exact category Complex Cotorsion pair Recollement |
| 本文献已被 维普 等数据库收录！ |
| 点击此处可从《数学年刊A辑(中文版)》浏览原始摘要信息 |
| 点击此处可从《数学年刊A辑(中文版)》下载免费的PDF全文 |
|
