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arXiv · 2509.01417

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

Tamar Datuashvili·Osman Mucuk·Nazmiye Alemdar·Tunçar Şahan
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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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Tamar Datuashvili, Osman Mucuk, Nazmiye Alemdar, Tunçar Şahan. 2025-09-01. Equivalence of the categories of categorical groups and cssc-crossed modules. https://arxiv.org/abs/2509.01417

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