{
  "id": "2310.11172",
  "version": "v1",
  "published": "2023-10-17T11:41:27.000Z",
  "updated": "2023-10-17T11:41:27.000Z",
  "title": "Dimensions and cotorsion pairs in recollements of extriangulated categories",
  "authors": [
    "Xin Ma",
    "Panyue Zhou"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "Let $(\\mathcal A, \\mathcal B, \\mathcal C)$ be a recollement of extriangulated categories. In this paper, we provide bounds on the coresolution dimensions of the subcategories involved in $\\mathcal A$, $\\mathcal B$ and $\\mathcal C$. We show that a hereditary cotorsion pair in $\\mathcal B$ can induce hereditary cotorsion pairs in $\\mathcal A$ and $\\mathcal C$ under certain conditions. Besides, we construct recollements of abelian categories from a recollement of extriangulated categories with respect to the hearts of cotorsion pairs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-17T11:41:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extriangulated categories",
      "induce hereditary cotorsion pairs",
      "coresolution dimensions",
      "abelian categories",
      "construct recollements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}