{
  "id": "0802.0663",
  "version": "v4",
  "published": "2008-02-05T16:48:51.000Z",
  "updated": "2011-07-18T22:19:44.000Z",
  "title": "Smooth Functors vs. Differential Forms",
  "authors": [
    "Urs Schreiber",
    "Konrad Waldorf"
  ],
  "comment": "75 pages, 1 figure; v2 with only minor changes; v3 has a layout improvement; v4 is the published version, with small improvements and a better proof of Lemma 2.6",
  "journal": "Homology, Homotopy Appl., 13(1), 143-203 (2011)",
  "categories": [
    "math.DG",
    "math.CT"
  ],
  "abstract": "We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory and differential geometry. We show that smooth 2-functors appear in several fields, namely as connections on (non-abelian) gerbes, as curvatures of smooth functors and as critical points in BF theory. We demonstrate further that our dictionary provides a powerful tool to discuss the transgression of geometric objects to loop spaces.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-07-18T22:19:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C05",
      "55R65",
      "18D05"
    ],
    "keywords": [
      "differential forms",
      "smooth functors",
      "smooth manifold",
      "loop spaces",
      "fundamental notions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 75,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.0663S"
    }
  }
}