An alternative description of symmetric monoidal categories, and symmetric 2-groups

Josep Elgueta

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arXiv · 2512.20717

An alternative description of symmetric monoidal categories, and symmetric 2-groups

Josep Elgueta

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Abstract

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.

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Josep Elgueta. 2025-12-23. An alternative description of symmetric monoidal categories, and symmetric 2-groups. https://arxiv.org/abs/2512.20717

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