适当阿贝尔子范畴的中间范畴

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI:10.1016/j.jpaa.2025.107892

Anders S. Kortegaard

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引用次数: 0

摘要

设A是一个三角化范畴T的扩展闭固有阿贝尔子范畴，它没有负1和2扩展。由此，在不需要t结构的情况下，可以构造出从ΣA A到A的两个函子，给出了一个蛇形引理与同源引理的镜像。我们将起源于Enomoto和Saito论文的中间范畴的概念推广到适当阿贝尔子范畴的集合，并证明在一定的假设下，这个集合与a中的无扭转类是双射的。

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Intermediate categories for proper abelian subcategories

Let

A

be an extension-closed proper abelian subcategory of a triangulated category

T

, with no negative 1 and 2 extensions. From this, two functors from

Σ A ⁎ A

A

can be constructed giving a snake lemma mirroring that of homology without needing a t-structure.

We generalize the concept of intermediate categories, which originates from a paper by Enomoto and Saito, to the setting of proper abelian subcategories and show that under certain assumptions this collection is in bijection with torsion-free classes in

A

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.