{
  "id": "1702.04070",
  "version": "v1",
  "published": "2017-02-14T04:06:12.000Z",
  "updated": "2017-02-14T04:06:12.000Z",
  "title": "Quillen equivalences between the model categories of smooth spaces, simplicial sets, and arc-gengerated spaces",
  "authors": [
    "Hiroshi Kihara"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1605.06794",
  "categories": [
    "math.AT"
  ],
  "abstract": "In the preceding paper, we have constructed a compactly generated model structure on the category $\\dcal$ of diffeological spaces together with the adjoint pairs $|\\ |_\\dcal : \\scal \\rightleftarrows \\dcal : S^\\dcal$ and $\\tilde{\\cdot} : \\dcal \\rightleftarrows \\ccal^0 : R$, where $\\scal$ and $\\ccal^0$ denote the category of simplicial sets and that of arc-generated spaces, respectively. In this paper, we show that $(|\\ |_\\dcal, S^\\dcal)$ and $(\\tilde{\\cdot}, R)$ are pairs of Quillen equivalences. Since our approach developed in the preceding paper applies to the category $\\ccal h$ of Chen spaces as well, $\\ccal h$ is also a compactly generated model category. We also show that the adjoint pair $\\mathfrak{S}_\\mathfrak{o} : \\ccal h \\rightleftarrows \\dcal : \\mathfrak{Ch}^\\sharp$ introduced by Stacey is a pair of Quillen equivalences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-14T04:06:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quillen equivalences",
      "simplicial sets",
      "smooth spaces",
      "arc-gengerated spaces",
      "adjoint pair"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}