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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月13日

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  • Antonio M. Cegarra

摘要

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.