{
  "id": "1005.1300",
  "version": "v2",
  "published": "2010-05-07T21:49:30.000Z",
  "updated": "2011-06-10T19:05:20.000Z",
  "title": "On the loop space of a 2-category",
  "authors": [
    "Matias L. del Hoyo"
  ],
  "comment": "21 pages, final version. Section 8 concerning the main theorem was rewritten. In particular, a partial converse for the main theorem was added",
  "journal": "Journal of Pure and Applied Algebra 216 (2012), pp. 28-40",
  "doi": "10.1016/j.jpaa.2011.05.001",
  "categories": [
    "math.AT"
  ],
  "abstract": "Every small category $C$ has a classifying space $BC$ associated in a natural way. This construction can be extended to other contexts and set up a fruitful interaction between categorical structures and homotopy types. In this paper we study the classifying space $B_2C$ of a 2-category $C$ and prove that, under certain conditions, the loop space $\\Omega_c B_2C$ can be recovered up to homotopy from the endomorphisms of a given object. We also present several subsidiary results that we develop to prove our main theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-10T19:05:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U10",
      "18D05",
      "55P35"
    ],
    "keywords": [
      "loop space",
      "classifying space",
      "small category",
      "natural way",
      "homotopy types"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1300D"
    }
  }
}