{
  "id": "1012.1541",
  "version": "v2",
  "published": "2010-12-07T16:00:25.000Z",
  "updated": "2011-01-04T17:21:01.000Z",
  "title": "In the category of relative categories the Rezk equivalences are exactly the DK-equivalences",
  "authors": [
    "C. Barwick",
    "D. M. Kan"
  ],
  "comment": "5 pages. Typographical errors corrected",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "In a previous paper we lifted Charles Rezk's complete Segal model structure on the category of simplicial spaces to a Quillen equivalent one on the category of \"relative categories,\" and our aim in this successor paper is to obtain a more explicit description of the weak equivalences in this model structure by showing that these weak equivalences are exactly the DK-equivalences, i.e. those maps between relative categories which induce a weak equivalence between their simplicial localizations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-04T17:21:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "relative categories",
      "rezk equivalences",
      "weak equivalence",
      "charles rezks complete segal model",
      "dk-equivalences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.1541B"
    }
  }
}