{
  "id": "2205.08401",
  "version": "v1",
  "published": "2022-05-17T14:34:54.000Z",
  "updated": "2022-05-17T14:34:54.000Z",
  "title": "Multifunctorial $K$-Theory is an Equivalence of Homotopy Theories",
  "authors": [
    "Niles Johnson",
    "Donald Yau"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AT",
    "math.CT",
    "math.KT"
  ],
  "abstract": "We show that each of the three $K$-theory multifunctors from small permutative categories to $\\mathcal{G}_*$-categories, $\\mathcal{G}_*$-simplicial sets, and connective spectra, is an equivalence of homotopy theories. For each of these $K$-theory multifunctors, we describe an explicit homotopy inverse functor. As a separate application of our general results about pointed diagram categories, we observe that the right-induced homotopy theory of Bohmann-Osorno $\\mathcal{E}_*$-categories is equivalent to the homotopy theory of pointed simplicial categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-17T14:34:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18M65",
      "55P42",
      "55P48",
      "18F25"
    ],
    "keywords": [
      "equivalence",
      "multifunctorial",
      "theory multifunctors",
      "explicit homotopy inverse functor",
      "simplicial sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}