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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.20717 |
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| _version_ | 1866918261884452864 |
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| author | Elgueta, Josep |
| author_facet | Elgueta, Josep |
| contents | An equivalent description of a symmetric monoidal category is introduced in which, instead of separate associator and commutator isomorphisms satisfying the usual coherence axioms, we simply have associo-commutator isomorphisms satisfying their own coherence laws. In particular, this yields an alternative description of a symmetric 2-group and leads to a cohomological classification of these objects in terms of Eilenberg-MacLane cubical cohomology for abelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An alternative description of symmetric monoidal categories, and symmetric 2-groups Elgueta, Josep Category Theory 18M05 An equivalent description of a symmetric monoidal category is introduced in which, instead of separate associator and commutator isomorphisms satisfying the usual coherence axioms, we simply have associo-commutator isomorphisms satisfying their own coherence laws. In particular, this yields an alternative description of a symmetric 2-group and leads to a cohomological classification of these objects in terms of Eilenberg-MacLane cubical cohomology for abelian groups. |
| title | An alternative description of symmetric monoidal categories, and symmetric 2-groups |
| topic | Category Theory 18M05 |
| url | https://arxiv.org/abs/2512.20717 |