{
  "abstract": "We prove that a coaction of a Hopf algebra on another preserving the latter's associative-algebra structure and comultiplication automatically also preserves the counit, antipode, and tensor-interchange map and in fact factors through the coaction dual to an action of an affine group scheme by Hopf-algebra automorphisms. This generalizes and unifies a number of results to the effect that quantum groups have only classical symmetries, due to Kasprzak et al., Budziński-Kasprzak and Brannan et al. The stated automatic classicality follows from the fact that the antipode, counit and tensorand-interchange of a Hopf algebra internal to any symmetric monoidal category are contained in the (non-symmetric) monoidal subcategory generated by the associative-algebra structure and the comultiplication, assuming a weak form of arrow-retraction invariance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01541",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexandru Chirvasitu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38qbebck3et2v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01541",
  "fulltext_url": null,
  "id": "38qbebck3et2v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01541",
  "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.CT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
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  "openalex": "W7206162780",
  "pdf_url": "https://arxiv.org/pdf/2609.01541",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38qbebck3et2v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.01541",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01541"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quantum Hopf rigidity in symmetric monoidal categories",
  "title_text": "Quantum Hopf rigidity in symmetric monoidal categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/38qbebck3et2v",
  "venue": "arXiv",
  "versions": []
}