Classification of Track (Bi)Categories via Group-Valued 3-Cocycles

IF 0.5 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2025-09-13 DOI:10.1007/s10485-025-09825-z

Antonio M. Cegarra

引用次数: 0

Abstract

Track bicategories, where each hom-category is a groupoid, appear in various mathematical and physical contexts. In this paper, we establish a cohomological classification of track bicategories and track categories using group-valued 3-cocycles on small categories, formulated as lax functors into the one-object 3-category of groups. In the abelian case, this classification aligns with Baues-Wirsching cohomology for small categories with coefficients in natural systems, recovering previously known classification results.

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基于群值3-环的轨道（Bi）类分类

跟踪双类别，其中每个人类别是一个群，出现在各种数学和物理环境中。本文利用小范畴上的群值3-环，建立了轨道双范畴和轨道范畴的上同调分类。在阿贝尔情况下，这种分类与自然系统中具有系数的小类别的Baues-Wirsching上同调一致，恢复了以前已知的分类结果。

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.