{
  "id": "1804.05045",
  "version": "v1",
  "published": "2018-04-13T17:22:19.000Z",
  "updated": "2018-04-13T17:22:19.000Z",
  "title": "Morita equivalences between algebraic dependent type theories",
  "authors": [
    "Valery Isaev"
  ],
  "comment": "32 pages",
  "categories": [
    "math.CT",
    "cs.LO",
    "math.LO"
  ],
  "abstract": "We define a notion of equivalence between algebraic dependent type theories which we call Morita equivalence. This notion has a simple syntactic description and an equivalent description in terms of models of the theories. The category of models of a type theory often carries a natural structure of a model category. If this holds for the categories of models of two theories, then a map between them is a Morita equivalence if and only if the adjunction generated by it is a Quillen equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-13T17:22:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "type theory",
      "algebraic dependent type theories",
      "morita equivalence",
      "simple syntactic description",
      "natural structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}