{
  "id": "0906.2393",
  "version": "v2",
  "published": "2009-06-12T18:15:54.000Z",
  "updated": "2010-06-26T22:11:12.000Z",
  "title": "Length 3 Complexes of Abelian Sheaves and Picard 2-Stacks",
  "authors": [
    "A. Emin Tatar"
  ],
  "comment": "46 pages, the proof of proposition 6.2 is added as appendix",
  "journal": "Advances in Mathematics, 225 (2011) 62-110",
  "doi": "10.1016/j.aim.2010.06.012",
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "We define a tricategory T of length 3 complexes of abelian sheaves, whose hom-bigroupoids consist of weak morphisms of such complexes. We also define a 3-category 2PIC(S) of Picard 2-stacks, whose hom-2-groupoids consist of additive 2-functors. We prove that these categories are triequivalent as tricategories. As a consequence we obtain a generalization of Deligne's analogous result about Picard stacks in SGA4, Exp. XVIII.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-26T22:11:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian sheaves",
      "picard stacks",
      "hom-bigroupoids consist",
      "weak morphisms",
      "delignes analogous result"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2393E"
    }
  }
}