{
  "abstract": "In this article, we first introduce the notion of BiHom-L-R-$\\binom{m,n,p,q}{s,t,u,v}$-smash biproduct over a BiHom-Hopf algebra, denoted by $D\\natural H$, where $m,n,p,q,s,t,u,v\\in \\mathbb{Z}$, and give the sufficient condition for $D\\natural H$ to be a BiHom-bialgebra. Furthermore, we describe the concept of BiHom-$\\binom{m,n,p,q}{s,t,u,v}$-Yetter-Drinfel'd-Long bimodule via BiHom-L-R-$\\binom{m,n,p,q}{s,t,u,v}$-smash biproduct bialgebra, and prove that the category $\\mathcal{LR}(H)(m,n,p,q)$ of BiHom-$\\binom{m,n,p,q}{s,t,u,v}$-Yetter-Drinfel'd-Long bimodule is a strict braided monoidal category. Finally, for a finite-dimensional BiHom-Hopf algebra H, \\(\\mathcal{LR}(H)\\binom{m,n,p,q}{s,t,u,v}\\) is isomorphic to the BiHom-$\\binom{s,t}{p,q}$-Yetter-Drinfel'd category \\({}_{H\\otimes H^*}^{H\\otimes H^*}\\mathcal{YD}\\binom{s,t}{p,q}\\) as braided monoidal categories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.26510",
  "author_total": 1,
  "authors": [
    {
      "name": "Dongdong Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3t19px5k3p1c7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.26510",
  "fulltext_url": null,
  "id": "3t19px5k3p1c7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.26510",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7171832822",
  "pdf_url": "https://arxiv.org/pdf/2607.26510",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3t19px5k3p1c7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2607.26510",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.26510"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "BiHom-L-R-smash biproduct and BiHom-Yetter-Drinfel'd-Long category",
  "title_text": "BiHom-L-R-smash biproduct and BiHom-Yetter-Drinfel'd-Long category",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/3t19px5k3p1c7",
  "venue": "arXiv",
  "versions": []
}