{
  "annotation_id": "18f0380d-ae46-4914-bcd9-30dbf495b13b",
  "date_created": "2026-03-02T18:01:25.096000Z",
  "date_modified": "2026-03-02T18:01:25.096000Z",
  "file_hash": "f28f83a0480ff356b2968374ef6569d0915b707543e4d299c80ec8d4a8066d92",
  "private": false,
  "record": {
    "abstract": "We define generalized bialgebras and Hopf algebras and on this basis we\nintroduce quantum categories and quantum groupoids. The quantization of the\ncategory of linear (super)spaces is constructed. We establish a criterion for\nthe classical value of the dimension of the polynomial function algebra on the\nfull subcategory of this quantum category specified by Sudbery type commutation\nrelations for quantum vector spaces (the ``Poincare -- Birkhoff -- Witt\nproperty\u0027\u0027). The criterion is the equality of the ``quantum constants\u0027\u0027\n$c_\\a=c_\\b^{\\pm 1}$ of the quantum vector spaces. (These constants appeared in\nearlier works on PBW for the multiparameter quantization of the general linear\ngroup.) Links with the Yang-Baxter equation and the Yang -- Baxter structures\nof quantum linear spaces are established. The role of categories as a\ngeneralization of groups is discussed.",
    "arxiv_id": "q-alg/9508005",
    "authors": [
      "Theodore Voronov"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Quantum categories. Quantization of the category of linear spaces",
    "url": "https://arxiv.org/abs/q-alg/9508005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e16acbc4-867b-45a5-bf6e-b48cc76a80bf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}