Year: 2026
Type: preprint
Abstract: Let $\mathcal{G}(G,A,α)$ be a discrete 2-group, given as the {categorical} extension of an ordinary group $G$ by an abelian group $A$. We define principal $\mathcal{G}$-bundles over a manifold in terms of Čech data over a good open cover. In the case of the manifold $S^2$, we calculate this bicategory explicitly, and identify its 2-skeleton. We compare with the holonomy bicategory $\mathrm{Fun}(*/\!\!/ π_{\le 2}(S^2), * /\!\!/ \mathcal{G})$, and provide a concrete equivalence between the two.
Source: arXiv (Cornell University)
Authors: Cliff, Emily, Lolelo, Yves, St-Cyr, Sandrine
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220948997