{
  "id": "2104.04924",
  "version": "v1",
  "published": "2021-04-11T05:46:20.000Z",
  "updated": "2021-04-11T05:46:20.000Z",
  "title": "Torsion pairs and recollements of extriangulated categories",
  "authors": [
    "Jian He",
    "Yonggang Hu",
    "Panyue Zhou"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "In this article, we prove that if $(\\mathcal A ,\\mathcal B,\\mathcal C)$ is a recollement of extriangulated categories, then torsion pairs in $\\mathcal A$ and $\\mathcal C$ can induce torsion pairs in $\\mathcal B$, and the converse holds under natural assumptions. Besides, we give mild conditions on a cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding abelian quotients to form a recollement of abelian categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-11T05:46:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G80",
      "18E10",
      "18E40"
    ],
    "keywords": [
      "extriangulated categories",
      "recollement",
      "induce torsion pairs",
      "corresponding abelian quotients",
      "converse holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}