{
  "id": "1902.03625",
  "version": "v1",
  "published": "2019-02-10T16:37:18.000Z",
  "updated": "2019-02-10T16:37:18.000Z",
  "title": "Derivator Six-Functor-Formalisms - Construction II",
  "authors": [
    "Fritz Hörmann"
  ],
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "Starting from very simple and obviously necessary axioms on a (derivator enhanced) four-functor-formalism, we construct derivator six-functor-formalisms using compactifications. This works, for example, for various contexts over topological spaces and algebraic schemes alike. The formalism of derivator six-functor-formalisms not only encodes all isomorphisms between compositions of the six functors (and their compatibilities) but also the interplay with pullbacks along diagrams and homotopy Kan extensions. One could say: a nine-functor-formalism. Such a formalism allows to extend six-functor-formalisms to stacks using (co)homological descent. The input datum can, for example, be obtained from a fibration of monoidal model categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-10T16:37:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U35",
      "14F05",
      "18D10",
      "18D30",
      "18E30",
      "18G99"
    ],
    "keywords": [
      "construction",
      "construct derivator six-functor-formalisms",
      "homotopy kan extensions",
      "monoidal model categories",
      "obviously necessary axioms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}