{
  "id": "1705.03863",
  "version": "v1",
  "published": "2017-05-10T17:27:43.000Z",
  "updated": "2017-05-10T17:27:43.000Z",
  "title": "Gabriel-Morita theory for excisive model categories",
  "authors": [
    "Clemens Berger",
    "Kruna Ratkovic"
  ],
  "comment": "43 pages",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "We develop a Gabriel-Morita theory for strong monads on pointed monoidal model categories. Assuming that the model category is excisive, i.e. the derived suspension functor is conservative, we show that if the monad T preserves cofibre sequences up to homotopy and has a weakly invertible strength, then the category of T-algebras is Quillen equivalent to the category of T(I)-modules where I is the monoidal unit. This recovers Schwede's theorem on connective stable homotopy over a pointed Lawvere theory as special case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-10T17:27:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G55",
      "18C15",
      "18D25",
      "55P42"
    ],
    "keywords": [
      "model category",
      "excisive model categories",
      "gabriel-morita theory",
      "preserves cofibre sequences",
      "pointed monoidal model categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}