{
  "abstract": "We develop a categorical framework for Lie-Rinehart monoids and their weak modules in a symmetric monoidal category. Using crossed homomorphisms, we construct a natural action of the monoidal category of modules over a Lie monoid on the category of weak Lie-Rinehart modules, thereby obtaining categorical versions of the Shen-Larsson functors. We further characterize the conditions under which the category of weak modules admits a monoidal structure and identify the corresponding condition for the associated functors to be strict monoidal. A dual theory for Lie- Rinehart comonoids and weak comodules is developed using cocrossed homomorphisms. Combining the module and comodule constructions, we obtain a bimodule category structure on the category of weak modules. Finally, we specialize the general framework to the symmetric monoidal category of super vector spaces, recovering Lie-Rinehart superalgebras and their associated Shen-Larsson-type constructions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21644",
  "author_total": 3,
  "authors": [
    {
      "name": "Han Dai"
    },
    {
      "name": "Vyacheslav Futorny"
    },
    {
      "name": "Huimin Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4rjt5g55jfdr0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21644",
  "fulltext_url": null,
  "id": "4rjt5g55jfdr0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21644",
  "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.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7213900450",
  "pdf_url": "https://arxiv.org/pdf/2609.21644",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4rjt5g55jfdr0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21644",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21644"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Categorical Lie-Rinehart modules and Shen-Larsson functors",
  "title_text": "Categorical Lie-Rinehart modules and Shen-Larsson functors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/4rjt5g55jfdr0",
  "venue": "arXiv",
  "versions": []
}