{
  "id": "1503.02720",
  "version": "v1",
  "published": "2015-03-09T22:43:21.000Z",
  "updated": "2015-03-09T22:43:21.000Z",
  "title": "The homotopy type of the $\\infty$-category associated to a simplicial complex",
  "authors": [
    "Dimitri Ara",
    "Georges Maltsiniotis"
  ],
  "comment": "68 pages, in French",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "This paper is part of a series of papers about homotopy theory of strict $n$-categories. In the first paper of this series, we gave conditions that guarantee the existence of a Thomason model category structure on the category of strict $n$-categories. The main goal of our paper is to show one of these conditions. To do so, we associate to any simplicial complex a strict $\\infty$-category generated by a computad. We conjecture that this $\\infty$-category has the same homotopy type as the corresponding simplicial complex and we prove this conjecture when the simplicial complex comes from a poset. We introduce the notion of a quasi-initial object of an $\\infty$-category and we show that Street's orientals admit such an object. One of the main tools used in this text is Steiner's theory of augmented directed complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-09T22:43:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18D05",
      "18G35",
      "18G55",
      "55P15",
      "55U10",
      "55U15"
    ],
    "keywords": [
      "homotopy type",
      "thomason model category structure",
      "streets orientals admit",
      "simplicial complex comes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 68,
      "language": "fr",
      "license": "arXiv",
      "status": "editable"
    }
  }
}