{
  "id": "2406.14031",
  "version": "v1",
  "published": "2024-06-20T06:51:10.000Z",
  "updated": "2024-06-20T06:51:10.000Z",
  "title": "Model structure arising from one hereditary cotorsion pair on extriangulated categories",
  "authors": [
    "Jiangsheng Hu",
    "Dongdong Zhang",
    "Panyue Zhou"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "Let $\\mathcal{C}$ be a weakly idempotent complete extriangulated category. In contrast with the Hovey correspondence of admissible model structures on weakly idempotent complete exact categories from two complete cotorsion pairs, we give a construction of model structures on $\\mathcal{C}$ from only one complete cotorsion pair. Our main result not only generalizes the work by Beligiannis-Reiten and Cui-Lu-Zhang, but also provides methods to construct model structures from silting objects of $\\mathcal{C}$ and co-$t$-structures in triangulated categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-20T06:51:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hereditary cotorsion pair",
      "model structure arising",
      "idempotent complete extriangulated category",
      "complete cotorsion pair",
      "weakly idempotent complete exact categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}