{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10402",
  "author_total": 3,
  "authors": [
    {
      "name": "Emily Cliff"
    },
    {
      "name": "Yves Lolelo"
    },
    {
      "name": "Sandrine St-Cyr"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a1mc849bc44db.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10402",
  "fulltext_url": null,
  "id": "a1mc849bc44db",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10402",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7220948997",
  "pdf_url": "https://arxiv.org/pdf/2610.10402",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a1mc849bc44db.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10402",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10402"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Flat principal 2-group bundles on $S^2$ and their holonomy",
  "title_text": "Flat principal 2-group bundles on S^2 and their holonomy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/a1mc849bc44db",
  "venue": "arXiv",
  "versions": []
}