2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77517We associate to a braided 2-stack ${\cal C}$ a torsor, endowed with a symmetric cube structure (or $Σ$-structure), whose triviality is equivalent to the existence on ${\cal C}$ of a fully symmetric monoidal structure. In order to perform the analogous construction for braided 4-stacks, it is necessary to introduce the notion of a $Γ_3$-torsor pair, which is in the same relation to cubic forms as torsors with $Σ$-structure are to quadratic ones.25 pages, Latex, xyPicCategory TheoryAlgebraic Geometry18D10, 19D23, 14K25text