张量外三角化范畴

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-08-07 DOI:10.1016/j.jalgebra.2025.07.041

Raphael Bennett-Tennenhaus , Isambard Goodbody , Janina C. Letz , Amit Shah

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引用次数: 0

摘要

张量外三角化范畴是具有与外三角化结构相容的对称单面结构的外三角化范畴。为此，我们定义了双三角化函子A×B→C的概念，其组成部分之间具有兼容性条件。我们有两个版本的兼容条件，更强的依赖于外三角化范畴的更高扩展。我们给出了张量外三角化范畴的许多例子。最后，我们将Balmer的厚张量理想分类推广到张量外三角化范畴。

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Tensor extriangulated categories

A tensor extriangulated category is an extriangulated category with a symmetric monoidal structure that is compatible with the extriangulated structure. To this end we define a notion of a biextriangulated functor

A \times B \to C

, with compatibility conditions between the components. We have two versions of compatibility conditions, the stronger depending on the higher extensions of the extriangulated categories. We give many examples of tensor extriangulated categories. Finally, we generalise Balmer's classification of thick tensor ideals to tensor extriangulated categories.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.