Equivalence of the categories of categorical groups and cssc-crossed modules
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912563887865856 |
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| author | Datuashvili, Tamar Mucuk, Osman Alemdar, Nazmiye Şahan, Tunçar |
| author_facet | Datuashvili, Tamar Mucuk, Osman Alemdar, Nazmiye Şahan, Tunçar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivalence of the categories of categorical groups and cssc-crossed modules Datuashvili, Tamar Mucuk, Osman Alemdar, Nazmiye Şahan, Tunçar Category Theory 18G45, 20L05, 18C40 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. |
| title | Equivalence of the categories of categorical groups and cssc-crossed modules |
| topic | Category Theory 18G45, 20L05, 18C40 |
| url | https://arxiv.org/abs/2509.01417 |