{
  "abstract": "The classical Dold--Kan correspondence identifies simplicial modules with connective chain complexes. Using Morita theory, we construct a Dold--Kan-type correspondence for every linear category carrying a suitable action of the maximum-preserving simplicial operators. The construction functorially assigns a Morita-equivalent normalized category to every such linear category. In particular, we obtain Dold--Kan-type correspondences for all crossed simplicial groups. We prove a rank formula for the normalized hom-modules and show that a crossed simplicial group is self-dual precisely when its underlying simplicial set of automorphism groups has dimension one. Furthermore, we construct normalization-compatible self-dualities and recover the Dwyer--Kan correspondence for duplicial, paracyclic and N-cyclic modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28138",
  "author_total": 1,
  "authors": [
    {
      "name": "Florian Warg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94qye99c5j176.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28138",
  "fulltext_url": null,
  "id": "94qye99c5j176",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28138",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
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      "arxiv",
      "math.CT"
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      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7223138923",
  "pdf_url": "https://arxiv.org/pdf/2610.28138",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94qye99c5j176.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28138",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28138"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Dold--Kan Correspondences via Morita Normalization",
  "title_text": "Dold--Kan Correspondences via Morita Normalization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/94qye99c5j176",
  "venue": "arXiv",
  "versions": []
}