{
  "id": "2409.18711",
  "version": "v1",
  "published": "2024-09-27T12:54:45.000Z",
  "updated": "2024-09-27T12:54:45.000Z",
  "title": "Recollements of thick subcategories",
  "authors": [
    "Yuxia Mei",
    "Li Wang",
    "Jiaqun Wei"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2012.03258",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $(\\mathcal{A}, \\mathcal{B}, \\mathcal{C}, i^{*}, i_{\\ast}, i^{!},j_!, j^\\ast, j_\\ast)$ be a recollement of extriangulated categories. We show that there is a bijection between thick subcategories in $\\mathcal{C}$ and thick subcategories in $\\mathcal{B}$ containing $i_{\\ast}\\mathcal{A}$. Futhermore, the thick subcategories $\\mathcal{V}$ in $\\mathcal{B}$ containing $i_{\\ast}\\mathcal{A}$ can induce a new recollement relative to $\\mathcal{A}$ and $j^{\\ast}\\mathcal{V}$. We also prove that silting subcategories in $\\mathcal{A}$ and $\\mathcal{C}$ can be glued to get silting subcategories in $\\mathcal{B}$ and the converse holds under certain conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-27T12:54:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thick subcategories",
      "recollement",
      "silting subcategories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}