{
  "id": "1903.09206",
  "version": "v1",
  "published": "2019-03-21T19:19:17.000Z",
  "updated": "2019-03-21T19:19:17.000Z",
  "title": "Representable presheaves of groups on the homotopy category of cocommutative dg-coalgebras and Tannakian reconstruction",
  "authors": [
    "Jaehyeok Lee",
    "Jae-Suk Park"
  ],
  "comment": "58pages",
  "categories": [
    "math.AG",
    "math.AT",
    "math.RT"
  ],
  "abstract": "Motivated by rational homotopy theory, we study a representable presheaf of groups $\\mathbf{\\mathfrak{P}}$ on the homotopy category of cocommutative differential graded coalgebras, its Lie algebraic counterpart and its linear representations. We prove a Tannaka type reconstruction theorem that $\\mathbf{\\mathfrak{P}}$ can be recovered from the dg-category of its linear representations along with the forgetful dg-functor to the underlying dg-category of chain complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-21T19:19:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homotopy category",
      "representable presheaf",
      "tannakian reconstruction",
      "cocommutative dg-coalgebras",
      "tannaka type reconstruction theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}