{
  "id": "1810.06496",
  "version": "v1",
  "published": "2018-10-15T16:16:33.000Z",
  "updated": "2018-10-15T16:16:33.000Z",
  "title": "A model structure on prederivators for $(\\infty,1)$-categories",
  "authors": [
    "Daniel Fuentes-Keuthan",
    "Magdalena Kedziorek",
    "Martina Rovelli"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "By theorems of Carlson and Renaudin, the theory of $(\\infty,1)$-categories embeds in that of prederivators. The purpose of this paper is to give a two-fold answer to the inverse problem: understanding which prederivators model $(\\infty,1)$-categories, either strictly or in a homotopical sense. First, we characterize which prederivators arise on the nose as prederivators associated to quasicategories. Next, we put a model structure on the category of prederivators and strict natural transformations, and prove a Quillen equivalence with the Joyal model structure for quasicategories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-15T16:16:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U35",
      "18G30",
      "18A25"
    ],
    "keywords": [
      "joyal model structure",
      "strict natural transformations",
      "categories embeds",
      "inverse problem",
      "prederivators model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}