{
  "abstract": "We study the construction of ternary semi-direct products in semi-abelian categories, following a definition of higher semi-direct product previously introduced by Carrasco and Cegarra for groups and Lie algebras. We show that these objects are determined by actions and equivariant morphisms satisfying a certain compatibility condition in the ambient category, and that actions by semi-direct products are a special case of this construction. We also show how their structure can be further simplified in algebraically coherent or locally algebraically cartesian closed categories. We also give a concrete description of the structure of ternary semi-direct products in concrete categories, and how our categorical interpretation of the necessary structure relates to the group and Lie-theoretic versions given by Carrasco and Cegarra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01671",
  "author_total": 1,
  "authors": [
    {
      "name": "Arnaud Duvieusart"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4k89879h8803c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01671",
  "fulltext_url": null,
  "id": "4k89879h8803c",
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  "landing_url": "https://arxiv.org/abs/2610.01671",
  "language": null,
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  "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"
    ],
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      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7215782315",
  "pdf_url": "https://arxiv.org/pdf/2610.01671",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4k89879h8803c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01671",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01671"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ternary semi-direct products in semi-abelian categories",
  "title_text": "Ternary semi-direct products in semi-abelian categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/4k89879h8803c",
  "venue": "arXiv",
  "versions": []
}