{
  "id": "2012.03258",
  "version": "v1",
  "published": "2020-12-06T13:18:30.000Z",
  "updated": "2020-12-06T13:18:30.000Z",
  "title": "Recollements of extriangulated categories",
  "authors": [
    "Li Wang",
    "Jiaqun Wei",
    "Haicheng Zhang"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT",
    "math.CT",
    "math.RA"
  ],
  "abstract": "We give a simultaneous generalization of recollements of abelian categories and triangulated categories, which we call recollements of extriangulated categories. For a recollement $(\\mathcal{A}$, $\\mathcal{B}$, $\\mathcal{C})$ of extriangulated categories, we show that cotorsion pairs in $\\mathcal{A}$ and $\\mathcal{C}$ induce cotorsion pairs in $\\mathcal{B}$ under certain conditions. As an application, our main result recovers a result given by Chen for recollements of triangulated categories, and it also shows a new phenomena when it is applied to abelian categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-06T13:18:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extriangulated categories",
      "recollement",
      "abelian categories",
      "induce cotorsion pairs",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}