{
  "abstract": "We develop an operadic theory of anti-splitting and anti-replicating for binary operads. For a binary operad $\\opd$, we define its anti-bisuccessor $\\ABSu(\\opd)$ and anti-trisuccessor $\\ATSu(\\opd)$. Each generating operation is recovered as the negative sum of two or three split operations, yielding canonical operad morphisms $\\opd\\to\\ABSu(\\opd)$ and $\\opd\\to\\ATSu(\\opd)$. For binary quadratic operads, these constructions are described by Manin black products: \\[ \\ABSu(\\opd)\\cong\\antiprelie\\bullet\\opd, \\qquad \\ATSu(\\opd)\\cong\\antipostlie\\bullet\\opd. \\] Dually, we also introduce the canonical quadratic anti-duplicator and anti-triplicator, together with their combinatorial counterparts defined by labeled planar binary trees. We show that they coincide precisely under a full-support condition. As applications, we obtain anti-dupli-com and anti-dupli-Lie algebras. We also display an example in which the two constructions differ. Furthermore, we establish the Koszul duality relations \\[ \\widehat{\\ADup}(\\opd^!) \\cong\\ABSu(\\opd)^!, \\qquad \\widehat{\\ATrip}(\\opd^!) \\cong\\ATSu(\\opd)^!, \\] providing an effective description of the canonical quadratic anti-duplicator in terms of the Manin white product. The framework recovers known constructions, including anti-dendriform, anti-pre-Lie and anti-pre-Poisson algebras, and produces further examples and Koszul dual pairs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21365",
  "author_total": 4,
  "authors": [
    {
      "name": "Chengming Bai"
    },
    {
      "name": "Li Guo"
    },
    {
      "name": "Yunhe Sheng"
    },
    {
      "name": "You Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d3g3nfrwya5k8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21365",
  "fulltext_url": null,
  "id": "d3g3nfrwya5k8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21365",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7222697192",
  "pdf_url": "https://arxiv.org/pdf/2610.21365",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d3g3nfrwya5k8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21365",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21365"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Anti-successors and anti-replicators, Manin products and Koszul duality",
  "title_text": "Anti-successors and anti-replicators, Manin products and Koszul duality",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:45Z",
  "url": "https://research.draconitic.com/paper/d3g3nfrwya5k8",
  "venue": "arXiv",
  "versions": []
}