The Commutant and Center of a Generalized Green Functor

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-09-25 DOI:10.1007/s10485-024-09785-w

Sael Cruz Cabello

引用次数: 0

Abstract

After fixing a commutative ring with unit R, we present the definition of adequate category and consider the category of R-linear functors from an adequate category to the category of R-modules. We endow this category of functors with a monoidal structure and study monoids (generalized Green functors) over it. For one of these generalized Green functors, we define two new monoids, its commutant and its center, and study some of their properties and relations between them. This work generalizes the article [3].

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广义绿色函数的换元和中心

在固定了具有单位 R 的交换环之后，我们提出了充分范畴的定义，并考虑了从充分范畴到 R 模块范畴的 R 线性函数范畴。我们赋予这个函子范畴以单元结构，并研究其上的单元（广义格林函子）。对于其中一个广义格林函子，我们定义了两个新的单体，即它的换元和它的中心，并研究了它们的一些性质和它们之间的关系。这项工作概括了文章[3]。

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

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.