Braided n-categories and $Σ$-structures

Details Braided n-categories and $Σ$-structures Braided n-categories and $Σ$-structures

1998-10-07

arxiv.org/abs/math/9810045v2

Mathematics

Category Theory

25 pages, Latex, xyPic

Scientific paper

We associate to a braided 2-stack ${\cal C}$ a torsor, endowed with a symmetric cube structure (or $\Sigma$-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 $\Gamma_3$-torsor pair, which is in the same relation to cubic forms as torsors with $\Sigma$-structure are to quadratic ones.

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