{
  "id": "1205.5527",
  "version": "v1",
  "published": "2012-05-24T18:49:11.000Z",
  "updated": "2012-05-24T18:49:11.000Z",
  "title": "Combinatorial realizability models of type theory",
  "authors": [
    "Pieter Hofstra",
    "Michael A. Warren"
  ],
  "comment": "38 pages",
  "categories": [
    "math.LO",
    "math.CT"
  ],
  "abstract": "We introduce a new model construction for Martin-L\\\"{o}f intensional type theory, which is sound and complete for the 1-truncated version of the theory. The model formally combines the syntactic model with a notion of realizability; it also encompasses the well-known Hofmann- Streicher groupoid semantics. As our main application, we use the model to analyse the syntactic groupoid associated to the type theory generated by a graph G, showing that it has the same homotopy type as the free groupoid generated by G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-24T18:49:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B15",
      "03G30"
    ],
    "keywords": [
      "combinatorial realizability models",
      "intensional type theory",
      "streicher groupoid semantics",
      "syntactic model",
      "free groupoid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5527H"
    }
  }
}