{
  "id": "1805.00374",
  "version": "v1",
  "published": "2018-05-01T14:56:26.000Z",
  "updated": "2018-05-01T14:56:26.000Z",
  "title": "Model category structures and spectral sequences",
  "authors": [
    "Joana Cirici",
    "Daniela Egas Santander",
    "Muriel Livernet",
    "Sarah Whitehouse"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi-isomorphism at a certain fixed stage of the associated spectral sequence. For filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and d\\'ecalage.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-01T14:56:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G55",
      "18G40"
    ],
    "keywords": [
      "model category structures",
      "filtered complexes",
      "cofibrantly generated model structures",
      "weak equivalences",
      "associated spectral sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}