Monoidal categories and multiextensions

Abstract

We show that the obstruction to the existence of a strict symmetric monoidal structure on a monoidal stack $\mathcal{C}$ is determined by a commutator biextension associated to $\mathcal{C}$, and that this biextension is alternating under an additional hypothesis. The analogous construction for monoidal 2-stacks is described, together with the corresponding generalizations of the concept of a biextension.

LaTeX, xy-pic, 38 pages