{
  "abstract": "Let $[0,1]_*$ be the unit interval $[0,1]$ equipped with a left-continuous t-norm $*$. We prove that $[0,1]_*\\text{-}\\mathbf{Set}$ is cartesian closed if and only if $*$ is the minimum t-norm. This extends the classification for continuous t-norms established in the first part of this work to the whole left-continuous setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05929",
  "author_total": 2,
  "authors": [
    {
      "name": "Lili Shen"
    },
    {
      "name": "Jian Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cc6qderytayjr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05929",
  "fulltext_url": null,
  "id": "cc6qderytayjr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05929",
  "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",
      "math.CT"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7211989690",
  "pdf_url": "https://arxiv.org/pdf/2609.05929",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cc6qderytayjr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05929",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05929"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cartesian closedness of the category of real-valued sets, II",
  "title_text": "Cartesian closedness of the category of real-valued sets, II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/cc6qderytayjr",
  "venue": "arXiv",
  "versions": []
}