三角分类上的平衡对

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2021-09-02 DOI:10.1142/s1005386723000329

X. Fu, Jiangsheng Hu, Dongdong Zhang, Hai-yan Zhu

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引用次数: 2

摘要

设[公式:见文本]为一个三角分类。我们首先在[公式:见文]中引入平衡对的概念，然后用足够的[公式:见文]-投射和[公式:见文]-注入建立平衡对与固有类[公式:见文]之间的双射对应关系。假设[公式:见文]是由平衡对[公式:见文]诱导的适当类。我们证明[公式:见文本]是一个三角化范畴。进一步证明了[公式:见文]是一个三角化范畴当且仅当[公式:见文]，且[公式:见文]是一个精确范畴当且仅当[公式:见文]。作为一种应用，我们提出了大量既不精确也不三角化的外三角化类别的例子。

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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Balanced Pairs on Triangulated Categories

Let [Formula: see text] be a triangulated category. We first introduce the notion of balanced pairs in [Formula: see text], and then establish the bijective correspondence between balanced pairs and proper classes [Formula: see text] with enough [Formula: see text]-projectives and [Formula: see text]-injectives. Assume that [Formula: see text] is the proper class induced by a balanced pair [Formula: see text]. We prove that [Formula: see text] is an extriangulated category. Moreover, it is proved that [Formula: see text] is a triangulated category if and only if [Formula: see text], and that [Formula: see text] is an exact category if and only if [Formula: see text]. As an application, we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.