{
  "id": "math/0301229",
  "version": "v1",
  "published": "2003-01-21T15:06:31.000Z",
  "updated": "2003-01-21T15:06:31.000Z",
  "title": "Homotopy theory of comodules over a Hopf algebroid",
  "authors": [
    "Mark Hovey"
  ],
  "comment": "43 pages",
  "categories": [
    "math.AT",
    "math.AG",
    "math.RA"
  ],
  "abstract": "Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for studying the homological algebra of comodules over a well-behaved Hopf algebroid (A, Gamma). That is, we construct the derived category Stable(Gamma) of (A, Gamma) as the homotopy category of a Quillen model structure on the category of unbounded chain complexes of Gamma-comodules. This derived category is obtained by inverting the homotopy isomorphisms, NOT the homology isomorphisms. We establish the basic properties of Stable(Gamma), showing that it is a compactly generated tensor triangulated category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-01-21T15:06:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U35",
      "55N22",
      "16W30",
      "18G55"
    ],
    "keywords": [
      "homotopy theory",
      "generated tensor triangulated category",
      "derived category",
      "quillen model structure",
      "unbounded chain complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1229H"
    }
  }
}