{
  "id": "2108.11952",
  "version": "v1",
  "published": "2021-08-26T17:59:24.000Z",
  "updated": "2021-08-26T17:59:24.000Z",
  "title": "Model categories for o-minimal geometry",
  "authors": [
    "Reid Barton",
    "Johan Commelin"
  ],
  "comment": "99 pages, 2 figures",
  "categories": [
    "math.AT",
    "math.CT",
    "math.LO"
  ],
  "abstract": "We introduce a model category of spaces based on the definable sets of an o-minimal expansion of a real closed field. As a model category, it resembles the category of topological spaces, but its underlying category is a coherent topos. We will show in future work that its cofibrant objects are precisely the \"weak polytopes\" of Knebusch.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-26T17:59:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U40",
      "03C64",
      "18F10",
      "55U35"
    ],
    "keywords": [
      "model category",
      "o-minimal geometry",
      "weak polytopes",
      "real closed field",
      "coherent topos"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 99,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}