Equivalence of the categories of categorical groups and cssc-crossed modules

2025/09/01 by Tamar Datuashvili, Datuashvili, Tamar, Osman Mucuk +5
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2509.01417

Abstract

In [8] we proved that any categorical group defines a c-crossed module, which is a cssc-crossed module defined in the same paper. In [9] we constructed a categorical group for any cssc-crossed module. In the presented paper we prove that these correspondences define functors between the corresponding categories, which realize an equivalence of the categories of categorical groups and cssc-crossed modules.

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