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

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.

28 pages. More detail has been added to the proof of Proposition 2.4, and an error in the proof of Proposition 2.12 has been corrected. Additional related work is also discussed