{
  "abstract": "We show that power semigroups of groups, and more generally reduced finitary power monoids, arise naturally as convolution monoids in Kleisli categories of powerset monads: (1) for the non-empty powerset monad, the Kleisli Hom-space $\\mathrm{Hom}_{\\mathbf{Kl}(\\mathscr P_+)}(1,G)$ is isomorphic to the power monoid $\\mathcal P_+(G)$; (2) for the reduced finite powerset monad on pointed sets, the Kleisli Hom-space $\\mathrm{Hom}_{\\mathbf{Kl}(\\mathscr P_{\\mathrm{fin}})}$ $(\\mathbb Z/2\\mathbb Z,H)$ is isomorphic to the reduced finitary power monoid $\\mathcal P_{\\mathrm{fin},1}(H)$. This unifies several constructions in power semigroup theory: Kleisli convolution representations of semigroups, base change along surjective group homomorphisms, and rigidity of automorphism groups. As an application, we prove that for every proper numerical monoid $S$, the Kleisli Hom-monoid $\\mathrm{Hom}_{\\mathbf{Kl}(\\mathscr P_{\\mathrm{fin}})}(\\mathbb Z/2\\mathbb Z,S)$ is rigid. This gives a proof of the Tringali--Yan conjecture in the language of Kleisli categories. It should be mentioned that this conjecture was already proved by Bhowmik and Tringali in a preprint posted on arXiv on July 25, 2026.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27292",
  "author_total": 3,
  "authors": [
    {
      "name": "Haicun Wen"
    },
    {
      "name": "Jian He"
    },
    {
      "name": "Yu-Zhe Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0znrezvjnt0v2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27292",
  "fulltext_url": null,
  "id": "0znrezvjnt0v2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27292",
  "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.CT"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7204592092",
  "pdf_url": "https://arxiv.org/pdf/2608.27292",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0znrezvjnt0v2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2608.27292",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27292"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Kleisli convolution representations of power monoids",
  "title_text": "Kleisli convolution representations of power monoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/0znrezvjnt0v2",
  "venue": "arXiv",
  "versions": []
}