{
  "abstract": "The category Nom of nominal sets was proposed by Pitts and Gabbay as a setting for the semantics of abstract syntax with variable bindings. It is well-known that Nom is a topos, also known as the Schanuel topos, and in particular it follows that Nom is locally closed, i.e., every slice category Nom/X is cartesian-closed. In this paper, we show that Nom has a much stronger property: every monoidal (closed) structure on Nom induces a monoidal (closed) structure on all slice categories Nom/X. One monoidal closed structure of particular interest on Nom is the separated product A * B, whose right adjoint A -* B is called the separated function space. In particular, it follows that Nom is locally separatedly closed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22551",
  "author_total": 3,
  "authors": [
    {
      "name": "Fahimeh Bayeh"
    },
    {
      "name": "Peng Fu"
    },
    {
      "name": "Peter Selinger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ewyp97xqeg4st.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22551",
  "fulltext_url": null,
  "id": "ewyp97xqeg4st",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22551",
  "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",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "openalex",
      "1702|Logic, programming, and type systems"
    ]
  ],
  "openalex": "W7214017996",
  "pdf_url": "https://arxiv.org/pdf/2609.22551",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ewyp97xqeg4st.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22551",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22551"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The category of nominal sets is locally monoidal closed",
  "title_text": "The category of nominal sets is locally monoidal closed",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/ewyp97xqeg4st",
  "venue": "arXiv",
  "versions": []
}