{
  "id": "2010.14869",
  "version": "v1",
  "published": "2020-10-28T10:33:25.000Z",
  "updated": "2020-10-28T10:33:25.000Z",
  "title": "$τ$-tilting theory in abelian categories",
  "authors": [
    "Yu Liu",
    "Panyue Zhou"
  ],
  "comment": "7 pages, comments are welcome",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "Let $\\mathcal A$ be a Hom-finite abelian category with enough projectives. In this note, we show that any covariantly finite $\\tau$-rigid subcategory is contained in a support $\\tau$-tilting subcategory. We also show that support $\\tau$-tilting subcategories are in bijection with certain finitely generated torsion classes. Some applications of our main results are also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-28T10:33:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tilting theory",
      "hom-finite abelian category",
      "tilting subcategory",
      "rigid subcategory",
      "finitely generated torsion classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}