{
  "abstract": "Cons-lists are fundamental to functional programming, and are well-understood as initial algebras, and as a concrete construction of free monoids. In category theory, such list objects can be axiomatised internal to any monoidal category, with nil and cons maps, and a recursion mechanism. When strengthened to support parametrised recursion, they can be shown to give the free monoid construction. We study a small variant on parametrised list objects called parametrised symmetric list objects, in a symmetric monoidal category, where the two frontmost elements are allowed to be permuted. We show that this gives a construction of free commutative monoids, and develop some related theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37944",
  "author_total": 3,
  "authors": [
    {
      "name": "Fiona Blackett"
    },
    {
      "name": "Vikraman Choudhury"
    },
    {
      "name": "Rin Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vhn52gt3kw7q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37944",
  "fulltext_url": null,
  "id": "4vhn52gt3kw7q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37944",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.CT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37944",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vhn52gt3kw7q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.37944",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37944"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Symmetric List Objects",
  "title_text": "Symmetric List Objects",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4vhn52gt3kw7q",
  "venue": "arXiv",
  "versions": []
}