{
  "id": "math/0007070",
  "version": "v1",
  "published": "2000-07-11T19:55:33.000Z",
  "updated": "2000-07-11T19:55:33.000Z",
  "title": "Universal homotopy theories",
  "authors": [
    "Daniel Dugger"
  ],
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these universal gadgets. The paper develops this formalism and discusses various applications, for instance to the study of homotopy colimits, the Dwyer-Kan theory of framings, and to the homotopy theory of schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-07-11T19:55:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homotopy theory",
      "universal homotopy theories",
      "model category",
      "formally adjoining homotopy colimits",
      "universal way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......7070D"
    }
  }
}