{
  "id": "1204.2013",
  "version": "v2",
  "published": "2012-04-10T00:15:26.000Z",
  "updated": "2012-04-24T00:16:14.000Z",
  "title": "Comparison of models for $(\\infty, n)$-categories, I",
  "authors": [
    "Julia E. Bergner",
    "Charles Rezk"
  ],
  "comment": "27 pages; updated references",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "While many different models for $(\\infty,1)$-categories are currently being used, it is known that they are Quillen equivalent to one another. Several higher-order analogues of them are being developed as models for $(\\infty, n)$-categories. In this paper, we establish model structures for some naturally arising categories of objects which should be thought of as $(\\infty,n)$-categories. Furthermore, we establish Quillen equivalences between them.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-24T00:16:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U35",
      "55U40",
      "18D05",
      "18D15",
      "18D20",
      "18G30",
      "18G55",
      "18C10"
    ],
    "keywords": [
      "comparison",
      "quillen equivalent",
      "establish quillen equivalences",
      "higher-order analogues",
      "establish model structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2013B"
    }
  }
}