{
  "id": "2006.09408",
  "version": "v1",
  "published": "2020-06-16T18:00:31.000Z",
  "updated": "2020-06-16T18:00:31.000Z",
  "title": "The coalgebraic enrichment of algebras in higher categories",
  "authors": [
    "Maximilien Péroux"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "We prove that given $\\mathcal{C}$ a presentably symmetric monoidal $\\infty$-category, and any essentially small $\\infty$-operad $\\mathcal{O}$, the $\\infty$-category of $\\mathcal{O}$-algebras in $\\mathcal{C}$ is enriched, tensored and cotensored over the presentably symmetric monoidal $\\infty$-category of $\\mathcal{O}$-coalgebras in $\\mathcal{C}$. We provide a higher categorical analogue of the universal measuring coalgebra. For categories in the usual sense, the result was proved by Hyland, L\\'{o}pez Franco, and Vasilakopoulou.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-16T18:00:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18D20",
      "18N70",
      "16T15"
    ],
    "keywords": [
      "higher categories",
      "coalgebraic enrichment",
      "presentably symmetric monoidal",
      "higher categorical analogue",
      "universal measuring coalgebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}