{
  "id": "2208.06381",
  "version": "v1",
  "published": "2022-08-12T17:12:34.000Z",
  "updated": "2022-08-12T17:12:34.000Z",
  "title": "Tilting Theory in exact categories",
  "authors": [
    "Julia Sauter"
  ],
  "comment": "26 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly: Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss standard results for tilting subcategories: Auslander correspondence, Bazzoni description of the perpendicular category. Secondly: We treat the question of induced derived equivalences separately - given a tilting subcategory T, we ask if a functor on the perpendicular category induces a derived equivalence to a (certain) functor category over T. If this is the case, we call the tilting subcategory ideq tilting. We prove a generalization of Miyashita's theorem (which is itself a generalization of a well-known theorem of Brenner-Butler) and characterize exact categories with enough projectives allowing ideq tilting subcategories. In particular, this is always fulfilled if the exact category is abelian with enough projectives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-12T17:12:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G15",
      "18G50",
      "18E99"
    ],
    "keywords": [
      "exact category",
      "tilting subcategory",
      "tilting theory",
      "arbitrary exact categories",
      "perpendicular category induces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}