{
  "id": "1304.3622",
  "version": "v1",
  "published": "2013-04-12T12:42:18.000Z",
  "updated": "2013-04-12T12:42:18.000Z",
  "title": "On model structure for coreflective subcategories of a model category",
  "authors": [
    "Tadayuki Haraguchi"
  ],
  "comment": "6 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $\\bf C$ be a coreflective subcategory of a cofibrantly generated model category $\\bf D$. In this paper we show that under suitable conditions $\\bf C$ admits a cofibrantly generated model structure which is left Quillen adjunct to the model structure on $\\bf D$. As an application, we prove that well-known convenient categories of topological spaces, such as $k$-spaces, compactly generated spaces, and $\\Delta$-generated spaces \\cite{DN} (called numerically generated in \\cite{KKH}) admit a finitely generated model structure which is Quillen equivalent to the standard model structure on the category $\\bf Top$ of topological spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-12T12:42:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U40",
      "55U35"
    ],
    "keywords": [
      "model category",
      "coreflective subcategory",
      "standard model structure",
      "topological spaces",
      "well-known convenient categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.3622H"
    }
  }
}