{
  "id": "2501.07140",
  "version": "v1",
  "published": "2025-01-13T08:58:45.000Z",
  "updated": "2025-01-13T08:58:45.000Z",
  "title": "Relative quasi-Gorensteinness in extriangulated categories",
  "authors": [
    "Zhenggang He"
  ],
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "Let $(\\mathcal{C},\\mathbb{E},\\mathfrak{s})$ be an extriangulated category with a proper class $\\xi$ of $\\mathbb{E}$-triangles. In this paper, we study the quasi-Gorensteinness of extriangulated categories. More precisely, we introduce the notion of quasi-$\\xi$-projective and quasi-$\\xi$-Gorenstein projective objects, investigate some of their properties and their behavior with respect to $\\mathbb{E}$-triangles. Moreover, we give some equivalent characterizations of objects with finite quasi-$\\xi$-Gorenstein projective dimension. As an application, our main results generalize Mashhad and Mohammadi's work in module categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-13T08:58:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E05",
      "18G05",
      "18G20",
      "18G25"
    ],
    "keywords": [
      "extriangulated category",
      "relative quasi-gorensteinness",
      "main results generalize mashhad",
      "proper class",
      "module categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}