Lawvere的Frobenius互易，Grandis的模连接和Dilworth的抽象主理想

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2025-05-16 DOI:10.1007/s10485-025-09808-0

Amartya Goswami, Zurab Janelidze, Graham Manuell

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引用次数: 0

摘要

这篇简短的笔记的目的是填补文献上的空白：学说理论中的Frobenius互易与射影同调代数中的模连接和抽象交换理想理论中的主元概念密切相关。这些概念是基于伽罗瓦连接的特殊性质，这些性质在类群结构的抽象研究中也起着重要的作用，从范畴/泛代数的角度来看；这种作用源于群论中一个经典而基本的结果：格同构定理。

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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Lawvere’s Frobenius Reciprocity, the Modular Connections of Grandis and Dilworth’s Abstract Principal Ideals

The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homological algebra and the notion of a principal element in abstract commutative ideal theory. These concepts are based on particular properties of Galois connections which play an important role also in the abstract study of group-like structures from the perspective of categorical/universal algebra; such role stems from a classical and basic result in group theory: the lattice isomorphism theorem.

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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.