{
  "id": "math/0404303",
  "version": "v1",
  "published": "2004-04-16T21:29:35.000Z",
  "updated": "2004-04-16T21:29:35.000Z",
  "title": "Completions of pro-spaces",
  "authors": [
    "Daniel C. Isaksen"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "For every ring R, we present a pair of model structures on the category of pro-spaces. In the first, the weak equivalences are detected by cohomology with coefficients in R. In the second, the weak equivalences are detected by cohomology with coefficients in all R-modules (or equivalently by pro-homology with coefficients in R). In the second model structure, fibrant replacement is essentially just the Bousfield-Kan R-tower. When R = Z/p, the first homotopy category is equivalent to a homotopy theory defined by Morel but has some convenient categorical advantages.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-16T21:29:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P60",
      "55N10",
      "18G55",
      "55U35"
    ],
    "keywords": [
      "pro-spaces",
      "completions",
      "weak equivalences",
      "coefficients",
      "second model structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4303I"
    }
  }
}