{
  "abstract": "We construct a categorification of the functor of grouplike elements of a Hopf algebra in the setting of braided monoidal categories. Given a braided bistrong monoidal functor admitting a right adjoint, we define a functor assigning to each Hopf monoid a group object obtained as a subobject of its underlying object by means of finite limits. We prove that this construction is functorial and provides a right adjoint to the induced free Hopf monoid functor, thereby extending the classical correspondence between groups and grouplike elements of Hopf algebras to a categorical setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14163",
  "author_total": 1,
  "authors": [
    {
      "name": "Frank Murphy-Hernandez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rcxqz76ekmgb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14163",
  "fulltext_url": null,
  "id": "0rcxqz76ekmgb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14163",
  "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": "W7213334905",
  "pdf_url": "https://arxiv.org/pdf/2609.14163",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rcxqz76ekmgb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14163",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14163"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Grouplike Functor and Monoidal Adjunctions",
  "title_text": "The Grouplike Functor and Monoidal Adjunctions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/0rcxqz76ekmgb",
  "venue": "arXiv",
  "versions": []
}