{
  "abstract": "We give a short proof that $κ$-cocompact objects in a presentable category are subterminal. As our main result, we extend this to the setting of presentable $\\infty$-categories. A consequence is that an $\\infty$-category $\\mathcal{C}$ such that both $\\mathcal{C}$ and $\\mathcal{C}^\\mathsf{op}$ are presentable is a small complete lattice, extending a classical theorem of Gabriel-Ulmer. Along the way, we prove a nilpotence result for phantom maps in general pointed presentable $\\infty$-categories. Additionally, we show that a strengthening of our main result is equivalent to the existence of a proper class of measurable cardinals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20533",
  "author_total": 3,
  "authors": [
    {
      "name": "Thorger Geiß"
    },
    {
      "name": "Phil Pützstück"
    },
    {
      "name": "Maxime Ramzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c468tp1vmpypf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20533",
  "fulltext_url": null,
  "id": "c468tp1vmpypf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20533",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
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      "arxiv",
      "math.CT"
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  "openalex": "W7213592966",
  "pdf_url": "https://arxiv.org/pdf/2609.20533",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c468tp1vmpypf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20533",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20533"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Cocompactness and Presentability",
  "title_text": "Cocompactness and Presentability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/c468tp1vmpypf",
  "venue": "arXiv",
  "versions": []
}