{
  "id": "1412.7289",
  "version": "v1",
  "published": "2014-12-23T08:52:50.000Z",
  "updated": "2014-12-23T08:52:50.000Z",
  "title": "From triangulated categories to module categories via homotopical algebra",
  "authors": [
    "Yann Palu"
  ],
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "The category of modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category C has been given two different descriptions: On the one hand, as shown by Osamu Iyama and Yuji Yoshino, it is equivalent to an ideal quotient of a subcategory of C. On the other hand, Aslak Buan and Robert Marsh proved that this module category is also equivalent to some localisation of C. In this paper, we give a conceptual interpretation, inspired from homotopical algebra, of this double description. Our main aim, yet to be acheived, is to generalise Buan-Marsh's result to the case of Hom-infinite cluster categories. We note that, contrary to the more common case where a model category is a module category whose homotopy category is triangulated, we consider here some triangulated categories whose homotopy categories are module categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-23T08:52:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "18G55",
      "13F60"
    ],
    "keywords": [
      "module category",
      "homotopical algebra",
      "homotopy category",
      "generalise buan-marshs result",
      "hom-infinite cluster categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.7289P"
    }
  }
}