相对于对偶对的Cartan-Eilenberg复形

吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (4): 787-792.

相对于对偶对的Cartan-Eilenberg复形

关佳瑷, 卢博

西北民族大学数学与计算机科学学院, 兰州 730030

收稿日期:2023-11-07 出版日期:2024-07-26 发布日期:2024-07-26
通讯作者: 卢博 E-mail:lubo55@126.com

Cartan-Eilenberg Complexes Relative to Duality Pairs

GUAN Jia’ai, LU Bo

College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China

Received:2023-11-07 Online:2024-07-26 Published:2024-07-26

摘要/Abstract

摘要： 设(A,B)是模范畴中的对偶对. 首先, 引入Cartan-Eilenberg-A复形和Cartan-Eilenberg-B复形的概念; 其次, 证明(C-E(A),C-E(B))是复形范畴中的对偶对, 其中C-E(A),C-E(B)分别表示所有Cartan-Eilenberg-A复形和Cartan-Eilenberg-B复形构成的类; 最后, 给出对偶对在复形上的应用.

关键词: 对偶对, Cartan-Eilenberg-A复形, Cartan-Eilenberg-B复形

Abstract: Let (A,B) be a duality pair in the category of modules. Firstly, the concepts of Cartan-Eilenberg-A and Cartan-Eilenberg-B complexes are introduced. Secondly, it is proven that (C-E(A),C-E(B)) is a duality pair in the category of complexes, where C-E(A) and C-E(B) denote the class of Cartan-Eilenberg-A complexes and Cartan-Eilenberg-B complexes, respectively. Finally, the application of duality pairs to complexes is given.

Key words: duality pair, Cartan-Eilenberg-A complex, Cartan-Eilenberg-B complex

中图分类号:

O154.2

关佳瑷, 卢博. 相对于对偶对的Cartan-Eilenberg复形[J]. 吉林大学学报(理学版), 2024, 62(4): 787-792.

GUAN Jia’ai, LU Bo. Cartan-Eilenberg Complexes Relative to Duality Pairs[J]. Journal of Jilin University Science Edition, 2024, 62(4): 787-792.

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