广义持久性和分级结构

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2021-02-12 DOI:10.4310/hha.2022.v24.n1.a2

Eero Hyry, Markus Klemetti

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引用次数: 1

摘要

我们研究了在索引集具有monoid作用的情况下，广义持久模和分次模之间的对应关系。我们引入了一个作用范畴的概念，作用范畴在一个单调分次环上。我们证明了从这个范畴到阿贝尔群范畴的加性函子的范畴同构于在具有幺拟作用的集合上分级的模的范畴，同构于在某个砸积上的酉模的范畴。此外，当索引集是偏序集时，我们为有限呈现的广义持久性模提供了一个新的刻画。

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Generalized persistence and graded structures

We investigate the correspondence between generalized persistence modules and graded modules in the case the indexing set has a monoid action. We introduce the notion of an action category over a monoid graded ring. We show that the category of additive functors from this category to the category of Abelian groups is isomorphic to the category of modules graded over the set with a monoid action, and to the category of unital modules over a certain smash product. Furthermore, when the indexing set is a poset, we provide a new characterization for a generalized persistence module being finitely presented.

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.