{
  "id": "1604.08480",
  "version": "v1",
  "published": "2016-04-28T15:53:29.000Z",
  "updated": "2016-04-28T15:53:29.000Z",
  "title": "On the equivalence between $Θ_{n}$-spaces and iterated Segal spaces",
  "authors": [
    "Rune Haugseng"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "We give a new proof of the equivalence between two of the main models for $(\\infty,n)$-categories, namely the $n$-fold Segal spaces of Barwick and the $\\Theta_{n}$-spaces of Rezk, by proving that these are algebras for the same monad on the $\\infty$-category of $n$-globular spaces. The proof works for a broad class of $\\infty$-categories that includes all $\\infty$-topoi.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-28T15:53:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18D05",
      "55U40"
    ],
    "keywords": [
      "iterated segal spaces",
      "equivalence",
      "fold segal spaces",
      "main models",
      "broad class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160408480H"
    }
  }
}