{
  "id": "math/0605200",
  "version": "v1",
  "published": "2006-05-08T13:17:26.000Z",
  "updated": "2006-05-08T13:17:26.000Z",
  "title": "Homotopy classification of gerbes",
  "authors": [
    "J. F. Jardine"
  ],
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "Gerbes are locally connected presheaves of groupoids. They are classified up to local weak equivalence by path components in a 2-cocycle category taking values in all sheaves of groups, their isomorphisms and homotopies. If F is a full presheaf of sheaves of groups, isomorphisms and homotopies, then [*,BF] is isomorphic to equivalence classes of gerbes locally equivalent to groups appearing in F. Giraud's non-abelian cohomology object of equivalence classes of gerbes with band L is isomorphic to morphisms in the homotopy category from the point * to the homotopy fibre over L for a map defined on BF and taking values in the classifying space for the stack completion of the fundamental groupoid of F.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-08T13:17:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homotopy classification",
      "girauds non-abelian cohomology object",
      "equivalence classes",
      "local weak equivalence",
      "fundamental groupoid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5200J"
    }
  }
}