A Recollement Approach to Cauchy Sequences and Cocompact Objects

IF 0.6 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-12-11 DOI:10.1007/s10468-025-10367-0

Nan Gao, Jing Ma, Yuxiao Yang

引用次数: 0

Abstract

In the paper, we identify Cauchy sequences and 0-cocompact objects along functors in the recollements of related categories, respectively. As applications in Gorenstein homological algebra, on one hand, the bounded Gorenstein derived categories of algebras of finite Cohen-Macaulay type are characterized as a sequential completion based on Cauchy sequences. On the other hand, the set of 0-cocompact cogenerators for the Gorenstein derived categories of algebras of finite Cohen-Macaulay type are obtained.

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柯西序列与紧致对象的回溯方法

在本文中，我们分别在相关范畴的集合中沿函子识别柯西序列和0-紧对象。作为在Gorenstein同调代数中的应用，一方面，有限Cohen-Macaulay型代数的有界Gorenstein派生范畴被表征为基于Cauchy序列的序列补全。另一方面，得到了有限Cohen-Macaulay型代数的Gorenstein派生范畴的0-紧协生集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.