{
  "abstract": "We show that for a 1-category C, the (ω, k)-polygraphic homology of C for any k {\\geq} 1, that is taken with cofibrant resolutions in strict (ω, k)- categories, does not depend on k and is canonically isomorphic to the homology of the classifying space of C. When C is a groupoid, we also show this for k = 0. In particular, this means that the classical homology of groups can be obtained by taking cofibrant resolutions in strict ω-groupoids. In order to show these results, we develop the theory of discrete Conduché fibrations in the category of strict (ω, k)-categories, building on previous work by the first-named author.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29967",
  "author_total": 2,
  "authors": [
    {
      "name": "Léonard Guetta"
    },
    {
      "name": "François Métayer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5fr2rxestetrj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29967",
  "fulltext_url": null,
  "id": "5fr2rxestetrj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29967",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214322994",
  "pdf_url": "https://arxiv.org/pdf/2609.29967",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5fr2rxestetrj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29967",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29967"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Groupoidal polygraphic homology",
  "title_text": "Groupoidal polygraphic homology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/5fr2rxestetrj",
  "venue": "arXiv",
  "versions": []
}