{
  "id": "0806.4160",
  "version": "v2",
  "published": "2008-06-25T17:44:32.000Z",
  "updated": "2009-06-17T17:18:00.000Z",
  "title": "Orbifolds as stacks?",
  "authors": [
    "Eugene Lerman"
  ],
  "comment": "v2: minor changes",
  "journal": "L'Enseign. Math. (2) 56 (2010), no. 3-4, 315--363",
  "categories": [
    "math.DG"
  ],
  "abstract": "The first goal of this survey paper is to argue that if orbifolds are groupoids, then the collection of orbifolds and their maps has to be thought of as a 2-category. Compare this with the classical definition of Satake and Thurston of orbifolds as a 1-category of sets with extra structure and/or with the \"modern\" definition of orbifolds as proper etale Lie groupoids up to Morita equivalence. The second goal is to describe two complementary ways of thinking of orbifolds as a 2-category: 1. the weak 2-category of foliation Lie groupoids, bibundles and equivariant maps between bibundles and 2. the strict 2-category of Deligne-Mumford stacks over the category of smooth manifolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-06-17T17:18:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "proper etale lie groupoids",
      "foliation lie groupoids",
      "equivariant maps",
      "survey paper",
      "definition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.4160L"
    }
  }
}