{
  "annotation_id": "3bce8b0f-56de-4809-893f-e2a494eaedaf",
  "date_created": "2026-02-17T05:53:15.434000Z",
  "date_modified": "2026-02-17T05:53:15.434000Z",
  "file_hash": "fcf56b283730e2a12d2ef8addda487e19b5ed68ff2ebd16ace8fc0a3c9f78ffa",
  "private": false,
  "record": {
    "abstract": "The algebraic formulation of the derivation and integration related by the First Fundamental Theorem of Calculus (FFTC) gives rise to the notion of differential Rota-Baxter algebra. The notion has a remarkable list of categorical properties, in terms of the existence of (co)extensions of differential and Rota-Baxter operators, of the lifting of monads and comonads, and of mixed distributive laws. Conversely, using these properties as axioms leads to a class of algebraic structures called para-differential Rota-Baxter algebras.\n  This paper carries out a systematic study of para-differential Rota-Baxter algebras. After their basic properties and examples from Hurwitz series and difference algebras, a Gr\\\"obner-Shirshov bases theory is established for para-differential Rota-Baxter algebras. Then an explicit construction of free para-differential Rota-Baxter algebras is obtained.",
    "arxiv_id": "2601.08249",
    "authors": [
      "Li Guo",
      "Aniruddha Talele",
      "Shilong Zhang",
      "Shanghua Zheng"
    ],
    "categories": [
      "math.RA",
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Para-differential Rota-Baxter algebras and their free objects by Gr\\\"obner-Shirshov bases",
    "url": "https://arxiv.org/abs/2601.08249",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3da3a39c-43b7-4b20-a6e6-fa22f28f105a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}