{
  "annotation_id": "196381b1-5c17-4049-930e-30fdc5b8911b",
  "date_created": "2026-03-02T18:01:28.531000Z",
  "date_modified": "2026-03-02T18:01:28.531000Z",
  "file_hash": "056722f93f7b65c7b8642a7bf80a8a1f9d344397abee2f9e42ce1e869bfe2a95",
  "private": false,
  "record": {
    "abstract": "Just as links may be algebraically described as certain morphisms in the\ncategory of tangles, compact surfaces smoothly embedded in R^4 may be described\nas certain 2-morphisms in the 2-category of `2-tangles in 4 dimensions\u0027. In\nthis announcement we give a purely algebraic characterization of the 2-category\nof unframed unoriented 2-tangles in 4 dimensions as the `free semistrict\nbraided monoidal 2-category with duals on one unframed self-dual object\u0027. A\nforthcoming paper will contain a proof of this result using the movie moves of\nCarter, Rieger and Saito. We comment on how one might use this result to\nconstruct invariants of 2-tangles.",
    "arxiv_id": "q-alg/9703033",
    "authors": [
      "John C. Baez",
      "Laurel Langford"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "journal_ref": "Lett. Math. Phys. 43 (1998), 187-197.",
    "title": "2-Tangles",
    "url": "https://arxiv.org/abs/q-alg/9703033"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "38f08ffc-9db3-4a9e-bf58-93933687c6bb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}