{
  "id": "1904.09797",
  "version": "v1",
  "published": "2019-04-22T10:52:42.000Z",
  "updated": "2019-04-22T10:52:42.000Z",
  "title": "Gorenstein dimension of abelian categories",
  "authors": [
    "Yu Liu",
    "Panyue Zhou"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "Let C be triangulated category and X a cluster tilting subcategory of C. Koenig and Zhu showed that the quotient category C/X is Gorenstein of Gorenstein dimension at most one. The notion of an extriangulated category was introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. Now let C be extriangulated category with enough projectives and enough injectives, and X a cluster tilting subcategory of C. In this article, we show that under certain conditions the quotient category C/X is Gorenstein of Gorenstein dimension at most one. As an application, this result generalizes work by Koenig and Zhu.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-22T10:52:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "18E10"
    ],
    "keywords": [
      "gorenstein dimension",
      "abelian categories",
      "quotient category c/x",
      "cluster tilting subcategory",
      "extriangulated category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}