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.
Keywords: symmetric monoidal category, symmetric 2-group, Eilenberg-MacLane cubical complex, abelian group cohomology
2020 MSC: 18M05, 18G45
Theory and Applications of Categories, Vol. 45, 2026, No. 43, pp 1782-1809.
Published 2026-08-03.
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