{
  "id": "1906.10989",
  "version": "v1",
  "published": "2019-06-26T11:44:28.000Z",
  "updated": "2019-06-26T11:44:28.000Z",
  "title": "Proper classes and Gorensteinness in extriangulated categories",
  "authors": [
    "Jiangsheng Hu",
    "Dongdong Zhang",
    "Panyue Zhou"
  ],
  "comment": "32pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. A notion of proper class in an extriangulated category is defined in this paper. Let $\\mathcal{C}$ be an extriangulated category and $\\xi$ a proper class in $\\mathcal{C}$. We prove that $\\mathcal{C}$ admits a new extriangulated structure. This construction gives extriangulated categories which are neither exact categories nor triangulated categories. Moreover, we introduce and study $\\xi$-Gorenstein projective objects in $\\mathcal{C}$ and demonstrate that $\\xi$-Gorenstein projective objects share some basic properties with Gorenstein projective objects in module categories or in triangulated categories. In particular, we refine a result of Asadollahi and Salarian [Gorenstein objects in triangulated categories, J. Algebra 281(2004), 264-286]. As an application, the $\\xi$-$\\mathcal{G}$projective model structures on extriangulated categories are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-26T11:44:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "18E10",
      "16E05",
      "18G20",
      "18G35"
    ],
    "keywords": [
      "extriangulated category",
      "proper class",
      "triangulated categories",
      "exact categories",
      "gorensteinness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}