{
  "abstract": "We develop a homotopy theory of directed graphs based on cubical homotopy groups, also known as $A$-groups or reduced GLMY homotopy groups. Localizing the category of directed graphs at morphisms that induce isomorphisms on these groups yields an $\\infty$-category, denoted by ${\\sf DGra}_\\infty$. We prove that ${\\sf DGra}_\\infty$ is equivalent to the $\\infty$-category of spaces, establishing a directed version of the discrete homotopy hypothesis of Carranza and Kapulkin.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.04959",
  "author_total": 5,
  "authors": [
    {
      "name": "Briony Eldridge"
    },
    {
      "name": "Sergei O. Ivanov"
    },
    {
      "name": "Xiaomeng Xu"
    },
    {
      "name": "Shing-Tung Yau"
    },
    {
      "name": "Mengmeng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/860wk65tgesfs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.04959",
  "fulltext_url": null,
  "id": "860wk65tgesfs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.04959",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.CO"
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    [
      "arxiv",
      "math.CT"
    ],
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      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7160490581",
  "pdf_url": "https://arxiv.org/pdf/2605.04959",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/860wk65tgesfs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2605.04959",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.04959"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The discrete homotopy hypothesis for directed graphs",
  "title_text": "The discrete homotopy hypothesis for directed graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/860wk65tgesfs",
  "venue": "arXiv",
  "versions": []
}