{
  "id": "2108.07964",
  "version": "v1",
  "published": "2021-08-18T03:54:17.000Z",
  "updated": "2021-08-18T03:54:17.000Z",
  "title": "Silting reduction in extriangulated categories",
  "authors": [
    "Yu Liu",
    "Panyue Zhou",
    "Yu Zhou",
    "Bin Zhu"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "We introduce pre-silting and silting subcategories in extriangulated categories and generalize the silting theory in triangulated categories. We prove that the silting reduction $\\mathcal B/({\\rm thick}\\mathcal W)$ of an extriangulated category $\\mathcal B$ with respect to a pre-silting subcategory $\\mathcal W$ can be realized as a certain subfactor category of $\\mathcal B$. This generalizes the result by Iyama-Yang. In particular, for a Gorenstein algebra, we get the relative version of the description of the singularity category due to Happel and Chen-Zhang by this reduction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-18T03:54:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extriangulated category",
      "silting reduction",
      "subfactor category",
      "singularity category",
      "gorenstein algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}