{
  "id": "1710.06414",
  "version": "v1",
  "published": "2017-10-17T17:44:17.000Z",
  "updated": "2017-10-17T17:44:17.000Z",
  "title": "Factorization homology of enriched $\\infty$-categories",
  "authors": [
    "David Ayala",
    "Aaron Mazel-Gee",
    "Nick Rozenblyum"
  ],
  "categories": [
    "math.AT",
    "math-ph",
    "math.CT",
    "math.MP",
    "math.QA"
  ],
  "abstract": "For an arbitrary symmetric monoidal $\\infty$-category $V$, we define the factorization homology of $V$-enriched $\\infty$-categories over (possibly stratified) 1-manifolds and study its basic properties. In the case that $V$ is \\textit{cartesian} symmetric monoidal, by considering the circle and its self-covering maps we obtain a notion of \\textit{unstable topological cyclic homology}, which we endow with an \\textit{unstable cyclotomic trace map}. As we show in \\cite{AMR-trace}, these induce their stable counterparts through linearization (in the sense of Goodwillie calculus).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-17T17:44:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "factorization homology",
      "arbitrary symmetric monoidal",
      "cyclotomic trace map",
      "goodwillie calculus",
      "topological cyclic homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}