{
  "id": "2409.08842",
  "version": "v1",
  "published": "2024-09-13T14:02:13.000Z",
  "updated": "2024-09-13T14:02:13.000Z",
  "title": "Contravariant Koszul duality between non-positive and positive dg algebras",
  "authors": [
    "Riku Fushimi"
  ],
  "comment": "30pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We characterize locally finite non-positive dg algebras that arise as Koszul duals of locally finite non-positive dg algebras. Moreover, we show that the Koszul dual functor induces contravariant derived equivalnces. As a consequence, we prove that every functorially finite bounded heart of $\\pvd A$ of a locally finite non-positive dg algebra is a length category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-13T14:02:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E35",
      "16E45",
      "16S37",
      "18G80"
    ],
    "keywords": [
      "locally finite non-positive dg algebra",
      "contravariant koszul duality",
      "positive dg algebras",
      "dual functor induces contravariant",
      "induces contravariant derived equivalnces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}