{
  "id": "1807.08226",
  "version": "v1",
  "published": "2018-07-22T02:15:15.000Z",
  "updated": "2018-07-22T02:15:15.000Z",
  "title": "Model Structures for Correspondences and Bifibrations",
  "authors": [
    "Danny Stevenson"
  ],
  "comment": "41 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "We study the notion of a bifibration in simplicial sets which generalizes the classical notion of two-sided discrete fibration studied in category theory. If $A$ and $B$ are simplicial sets we equip the category of simplicial sets over $A\\times B$ with the structure of a model category for which the fibrant objects are the bifibrations from $A$ to $B$. We also equip the category of correspondences of simplicial sets from $A$ to $B$ with the structure of a model category. We describe several Quillen equivalences relating these model structure with the covariant model structure on the category of simplicial sets over $B^{\\mathrm{op}}\\times A$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-22T02:15:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U35",
      "18G30",
      "18G55"
    ],
    "keywords": [
      "simplicial sets",
      "bifibration",
      "correspondences",
      "model category",
      "covariant model structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}