{
  "abstract": "Cartesian 2-fibrations provide a way to understand indexed categories, but their classical ``straightening'' construction requires several layers of weak coherence data. This paper develops a homotopical framework that replaces much of this bookkeeping with a fully strict model. By using marked 2-categories to record the cartesian morphisms and 2-cells, we construct a model structure whose fibrant objects are precisely the cartesian 2-fibrations over a fixed 2-category $\\mathcal{C}$. We then show that the marked Grothendieck construction identifies these 2-fibrations, up to weak equivalence, with strict 2-functors from $\\mathcal{C}$ into $2\\mathrm{Cat}$. As an additional contribution, we construct localizations of 2-categories that simultaneously invert selected morphisms and 2-cells.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11759",
  "author_total": 6,
  "authors": [
    {
      "name": "Cesar Bardomiano Martinez"
    },
    {
      "name": "Jana K. Nickel"
    },
    {
      "name": "Maru Sarazola"
    },
    {
      "name": "Daniel Teixeira"
    },
    {
      "name": "Santiago Toro Oquendo"
    },
    {
      "name": "Paula Verdugo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/770a30nbdkty0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11759",
  "fulltext_url": null,
  "id": "770a30nbdkty0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11759",
  "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": "W7212259272",
  "pdf_url": "https://arxiv.org/pdf/2609.11759",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/770a30nbdkty0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11759",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11759"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A model structure for cartesian 2-fibrations",
  "title_text": "A model structure for cartesian 2-fibrations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/770a30nbdkty0",
  "venue": "arXiv",
  "versions": []
}