{
  "id": "2412.10359",
  "version": "v1",
  "published": "2024-12-13T18:52:37.000Z",
  "updated": "2024-12-13T18:52:37.000Z",
  "title": "Modeling $(\\infty,1)$-categories with Segal spaces",
  "authors": [
    "Lyne Moser",
    "Joost Nuiten"
  ],
  "comment": "20 pages; comments welcome",
  "categories": [
    "math.AT"
  ],
  "abstract": "In this paper, we construct a model structure for $(\\infty,1)$-categories on the category of simplicial spaces, whose fibrant objects are the Segal spaces. In particular, we show that it is Quillen equivalent to the models of $(\\infty,1)$-categories given by complete Segal spaces and Segal categories. We furthermore prove that this model structure has desirable properties: it is cartesian closed and left proper. As applications, we get a simple description of the inclusion of categories into $(\\infty,1)$-categories and of homotopy limits of $(\\infty,1)$-categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-13T18:52:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18N60",
      "55U35",
      "18N50"
    ],
    "keywords": [
      "model structure",
      "complete segal spaces",
      "fibrant objects",
      "homotopy limits",
      "simplicial spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}