{
  "id": "math/0612549",
  "version": "v2",
  "published": "2006-12-19T13:55:06.000Z",
  "updated": "2008-08-01T09:36:02.000Z",
  "title": "Two-Categorical Bundles and Their Classifying Spaces",
  "authors": [
    "Nils. A. Baas",
    "Marcel Bokstedt",
    "Tore August Kro"
  ],
  "comment": "LaTex, 64 pages, revised version",
  "categories": [
    "math.AT",
    "math.CT",
    "math.KT"
  ],
  "abstract": "For a 2-category 2C we associate a notion of a principal 2C-bundle. In case of the 2-category of 2-vector spaces in the sense of M.M. Kapranov and V.A. Voevodsky this gives the the 2-vector bundles of N.A. Baas, B.I. Dundas and J. Rognes. Our main result says that the geometric nerve of a good 2-category is a classifying space for the associated principal 2-bundles. In the process of proving this we develop a lot of powerful machinery which may be useful in further studies of 2-categorical topology. As a corollary we get a new proof of the classification of principal bundles. A calculation based on the main theorem shows that the principal 2-bundles associated to the 2-category of 2-vector spaces in the sense of J.C. Baez and A.S. Crans split, up to concordance, as two copies of ordinary vector bundles. When 2C is a cobordism type 2-category we get a new notion of cobordism-bundles which turns out to be classified by the Madsen-Weiss spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-01T09:36:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R65",
      "18D05",
      "19D99"
    ],
    "keywords": [
      "classifying space",
      "two-categorical bundles",
      "ordinary vector bundles",
      "main result says",
      "madsen-weiss spaces"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12549B"
    }
  }
}