{
  "abstract": "We develop a higher-geometric framework for magnetic higher-form symmetries of pre-quantum field theories. The magnetic (topological) charges of a sigma-model with stacky target are encoded by the shape of the target, equivalently of its stack of fields, which is op-dual to the flat automorphism group controlling electric symmetries. Magnetic symmetry backgrounds are obtained by dualizing these charges against a chosen moduli stack of topological field theories, generalizing Pontryagin duality, and act on the theory by stacking. Cohesive modalities allow for targets with non-finite and non-discrete data. When the dualizing stack is a grouplike $E_\\infty$-object, we prove a fibration theorem expressing the magnetic symmetries of an electrically gauged theory in terms of those of the ungauged theory and of the gauge group, computed by a homotopy-fixed-point spectral sequence with an explicit first page. For moduli stacks of higher $U(1)$-gerbes with connection, encoding bulk topological local Lagrangians, we prove a factorization theorem: the magnetic symmetry backgrounds of any connected target split, non-canonically, into Pontryagin duals of its integral homology groups, and are necessarily flat, as a consequence of dualizing discrete charges against a target with connections. We illustrate both theorems with pure $\\mathrm{Pin}^\\pm(2)$ gauge theory: $O(2)$ carries invertible magnetic $\\mathbb{Z}_2$ symmetries in form degrees $d-3$, $d-4$ and $d-5$ that are absent for $\\mathrm{Pin}^-(2)$, the first two distinguished by a single differential of the spectral sequence. Gauging and physical applications are developed in upcoming work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03865",
  "author_total": 1,
  "authors": [
    {
      "name": "Alonso Perez-Lona"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01ej402m66xyy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03865",
  "fulltext_url": null,
  "id": "01ej402m66xyy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03865",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7220649911",
  "pdf_url": "https://arxiv.org/pdf/2610.03865",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01ej402m66xyy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.03865",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03865"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Magnetic Higher-Form Symmetries as Dual Fundamental $\\infty$-Groupoids",
  "title_text": "Magnetic Higher-Form Symmetries as Dual Fundamental ∞-Groupoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/01ej402m66xyy",
  "venue": "arXiv",
  "versions": []
}