{
  "abstract": "We study several fundamental properties of the category $\\mathbf{Kur}$ introduced in \\cite{Kim1}. By defining fibrations and weak equivalences, we show that morphisms with manifold targets admit homotopy fiber products; this is then applied to obtain a notion of generalized intersections of two submanifolds. A definition of the Weinstein category in the context of Kuranishi spaces is also presented. Finally, we establish that $\\mathbf{Kur}$ forms a category of fibrant objects in the sense of Brown \\cite{Brown}, and discuss its homotopy category $\\operatorname{Ho}(\\mathbf{Kur})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11594",
  "author_total": 1,
  "authors": [
    {
      "name": "Taesu Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3dzpnyctykcgj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11594",
  "fulltext_url": null,
  "id": "3dzpnyctykcgj",
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  "landing_url": "https://arxiv.org/abs/2610.11594",
  "language": null,
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
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    [
      "arxiv",
      "math.AT"
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      "arxiv",
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      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7221134654",
  "pdf_url": "https://arxiv.org/pdf/2610.11594",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3dzpnyctykcgj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11594",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11594"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
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  ],
  "title": "Kuranishi spaces in a category of fibrant objects and their homotopy fiber products",
  "title_text": "Kuranishi spaces in a category of fibrant objects and their homotopy fiber products",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/3dzpnyctykcgj",
  "venue": "arXiv",
  "versions": []
}