{
  "abstract": "In previous work, we analysed a number of categorical properties, of interest in the context of Janelidze-Márki-Tholen semi-abelian categories, for the variety $\\mathsf{HSLat}$ of Heyting semilattices. In this paper, we focus on the subvariety $\\mathsf{ELHSLat}$ of equationally linear Heyting semilattices. Our main objective is to show that, unlike $\\mathsf{HSLat}$, this category is algebraically coherent. We furthermore prove that it is neither locally algebraically cartesian closed nor cosmash associative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24325",
  "author_total": 5,
  "authors": [
    {
      "name": "Xabier García-Martínez"
    },
    {
      "name": "James R. A. Gray"
    },
    {
      "name": "Michael A. Hoefnagel"
    },
    {
      "name": "Tim Van der Linden"
    },
    {
      "name": "Corentin Vienne"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jhz07dfxk29w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24325",
  "fulltext_url": null,
  "id": "1jhz07dfxk29w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24325",
  "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.CT"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7214013847",
  "pdf_url": "https://arxiv.org/pdf/2609.24325",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jhz07dfxk29w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24325"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Observations on the variety of equationally linear Heyting semilattices",
  "title_text": "Observations on the variety of equationally linear Heyting semilattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/1jhz07dfxk29w",
  "venue": "arXiv",
  "versions": []
}