{
  "id": "0810.3063",
  "version": "v3",
  "published": "2008-10-17T06:16:12.000Z",
  "updated": "2011-06-10T19:40:56.000Z",
  "title": "On the homotopy type of a cofibred category",
  "authors": [
    "Matias L. del Hoyo"
  ],
  "comment": "27 pages, corrected version",
  "journal": "Cahiers de Topologie et Geometrie Differentielle Categoriques 53 (2012), no. 2, pp. 82-114",
  "categories": [
    "math.AT"
  ],
  "abstract": "In this paper we describe two ways on which cofibred categories give rise to bisimplicial sets. The \"fibred nerve\" is a natural extension of Segal's classical nerve of a category, and it constitutes an alternative simplicial description of the homotopy type of the total category. If the fibration is splitting, then one can construct the \"cleaved nerve\", a smaller variant which emerges from a distinguished closed cleavage. We interpret some classical theorems by Thomason and Quillen in terms of our constructions, and use the fibred and cleaved nerve to establish new results on homotopy and homology of small categories.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-06-10T19:40:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18D30",
      "18G30",
      "55U35"
    ],
    "keywords": [
      "homotopy type",
      "cofibred category",
      "cleaved nerve",
      "total category",
      "bisimplicial sets"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.3063D"
    }
  }
}