{
  "id": "2506.16188",
  "version": "v1",
  "published": "2025-06-19T10:07:43.000Z",
  "updated": "2025-06-19T10:07:43.000Z",
  "title": "Mutation of $n$-cotorsion pairs in extriangulated categories",
  "authors": [
    "Huimin Chang",
    "Yu Liu",
    "Panyue Zhou"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "In this article, we introduce the notion of $n$-cotorsion pairs in extriangulated categories, which extends both the cotorsion pairs established by Nakaoka and Palu and the $n$-cotorsion pairs in triangulated categories developed by Chang and Zhou. We further prove that any mutation of an $n$-cotorsion pair remains an $n$-cotorsion pair. As applications, we provide a geometric characterization of $n$-cotorsion pairs in $n$-cluster categories of type $A_{\\infty}$, and we realize mutations of $n$-cotorsion pairs geometrically via rotations of certain configurations of $n$-admissible arcs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-19T10:07:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extriangulated categories",
      "cotorsion pair remains",
      "geometric characterization",
      "cluster categories",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}