{
  "id": "math/0610009",
  "version": "v4",
  "published": "2006-09-30T01:12:09.000Z",
  "updated": "2009-02-08T15:40:18.000Z",
  "title": "Cofibrations in Homotopy Theory",
  "authors": [
    "Andrei Radulescu-Banu"
  ],
  "comment": "Ams-latex, 158 pages. Corrections to Thm. 6.4.1 and Def. 7.2.5",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "We define Anderson-Brown-Cisinski (ABC) cofibration categories, and construct homotopy colimits of diagrams of objects in ABC cofibration categories. Homotopy colimits for Quillen model categories are obtained as a particular case. We attach to each ABC cofibration category a left Heller derivator. A dual theory is developed for homotopy limits in ABC fibration categories and for right Heller derivators. These constructions provide a natural framework for 'doing homotopy theory' in ABC (co)fibration categories.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-02-08T15:40:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G55",
      "55U35",
      "18G10",
      "18G30",
      "55U10"
    ],
    "keywords": [
      "homotopy theory",
      "abc cofibration category",
      "construct homotopy colimits",
      "right heller derivators",
      "quillen model categories"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 158,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10009R"
    }
  }
}