{
  "id": "1504.04007",
  "version": "v1",
  "published": "2015-04-15T19:58:52.000Z",
  "updated": "2015-04-15T19:58:52.000Z",
  "title": "Factorization homology from higher categories",
  "authors": [
    "David Ayala",
    "John Francis",
    "Nick Rozenblyum"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AT",
    "math.CT",
    "math.GT",
    "math.QA"
  ],
  "abstract": "We construct a pairing, which we call factorization homology, between framed manifolds and higher categories. The essential geometric notion is that of a vari-framing of a stratified manifold, which is a framing on each stratum together with a coherent system of compatibilities of framings along links of strata. Our main result constructs labeling systems on disk-stratified vari-framed $n$-manifolds from $(\\infty,n)$-categories. These $(\\infty,n)$-categories, in contrast with the literature to date, are not required to have adjoints. The core calculation supporting this result is a homotopy equivalence between the space of conically smooth diffeomorphisms of a disk-stratified manifold and its space of vari-framings. This allows the following conceptual definition: the factorization homology \\[ \\int_M\\mathcal{C} \\] of a framed $n$-manifold $M$ with coefficients in an $(\\infty,n)$-category $\\mathcal{C}$ is the classifying space of $\\mathcal{C}$-labeled disk-stratifications over $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-15T19:58:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "factorization homology",
      "higher categories",
      "main result constructs labeling systems",
      "essential geometric notion",
      "coherent system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150404007A",
      "inspire": 1359982
    }
  }
}