{
  "abstract": "We construct a diagrammatic presentation by generators and relations for all dihedral pointed fusion categories $\\mathrm{Vec}_{\\mathrm{D}_{2n}}^ω$. Applying a jellyfish algorithm on our diagrammatics, we obtain an explicit closed formula for a complete set of normalized 3-cocycle representatives of $\\mathrm{D}_{2n}$. As applications of our diagrammatics, we prove a universal property and show that in some cases we can recover affine $A$ unshaded subfactor planar algebras. We then extend our presentation to obtain diagrammatics for all pivotal structures on $\\mathrm{Vec}_{\\mathrm{D}_{2n}}^ω$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40498",
  "author_total": 2,
  "authors": [
    {
      "name": "Agustina Czenky"
    },
    {
      "name": "Melody Molander"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvwn9sdm1msw2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40498",
  "fulltext_url": null,
  "id": "cvwn9sdm1msw2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40498",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40498",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvwn9sdm1msw2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40498",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40498"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Dihedral pointed fusion categories: diagrammatics, 3-cocycle representatives, and planar algebras",
  "title_text": "Dihedral pointed fusion categories: diagrammatics, 3-cocycle representatives, and planar algebras",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/cvwn9sdm1msw2",
  "venue": "arXiv",
  "versions": []
}