{
  "abstract": "Evidence suggests a tight connection between the existence of antipode-like maps on bialgebra-like structures, and the Frobenius property for the associated free Hopf module functor. In this paper, we prove that in any braided monoidal category satisfying few mild assumptions, a bimonoid is a one-sided Hopf monoid and the antipode is a bimonoid anti-homomorphism, if and only if the free Hopf module functor is Frobenius. Our interest in these structures stems from having found genuine examples of one-sided Hopf monoids in contexts where the braiding is non-trivial. In fact, we provide a construction of the free one-sided Hopf monoid over a comonoid in any symmetric monoidal category with some non-restrictive additional assumptions. We present several examples of this construction, and describe the resulting one-sided (sometimes two-sided) Hopf monoids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13028",
  "author_total": 3,
  "authors": [
    {
      "name": "Lucrezia Bottegoni"
    },
    {
      "name": "Davide Ferri"
    },
    {
      "name": "Paolo Saracco"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6szkh7vh1zwn3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13028",
  "fulltext_url": null,
  "id": "6szkh7vh1zwn3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13028",
  "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"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7212520390",
  "pdf_url": "https://arxiv.org/pdf/2609.13028",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6szkh7vh1zwn3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13028",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13028"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Frobenius functors and one-sided Hopf algebras in braided monoidal categories",
  "title_text": "Frobenius functors and one-sided Hopf algebras in braided monoidal categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/6szkh7vh1zwn3",
  "venue": "arXiv",
  "versions": []
}