{
  "abstract": "A tensor product is known for commutative Rota--Baxter algebras through a universal construction, but its underlying algebra need not be the ordinary tensor product $A\\otimes B$ and can be substantially larger. We show that, after passing to augmented Rota--Baxter algebras, the ordinary tensor product itself carries a natural Rota--Baxter operator which makes the category monoidal with the usual associator and unit constraints. The resulting structure is intrinsically nonsymmetric: over a field of characteristic zero, this operator and its flip-conjugated counterpart are the only possibilities among linear combinations of five natural terms, while over any field the full category admits no braiding. Its comonoid objects are precisely Rota--Baxter cocycle bialgebras. Moreover, the free Rota--Baxter adjunction yields a bimonad and free cocycle bialgebras on ordinary bialgebras, with compatible Hopf structures for connected filtered inputs, in both the associative and commutative settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17525",
  "author_total": 3,
  "authors": [
    {
      "name": "Li Guo"
    },
    {
      "name": "Yunzhou Xie"
    },
    {
      "name": "Yi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b233dgpawznrc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17525",
  "fulltext_url": null,
  "id": "b233dgpawznrc",
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  "landing_url": "https://arxiv.org/abs/2610.17525",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
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  "openalex": "W7221804947",
  "pdf_url": "https://arxiv.org/pdf/2610.17525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b233dgpawznrc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Monoidal structure on Rota-Baxter algebras via augmentation, and free cocycle bialgebras",
  "title_text": "Monoidal structure on Rota-Baxter algebras via augmentation, and free cocycle bialgebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/b233dgpawznrc",
  "venue": "arXiv",
  "versions": []
}