{
  "abstract": "Let $Q$ be a commutative unital quantale and $\\QRel$ the ordered category of sets and $Q$-relations. We develop a categorical foundation for formal and property-oriented concept lattices of $Q$-relations via the diagonal category $\\DQRel$ and back-diagonal category $\\BQRel$. Our main results are: (1) the formal concept lattice construction is induced by a representable functor on $\\BQRel$; (2) the property-oriented concept lattice construction corresponds to a representable functor on $\\DQRel$; and (3) for regular $Q$-relations, the property-oriented concept lattice of their pointwise tensor product is naturally isomorphic to the tensor product of the respective property-oriented concept lattices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13809",
  "author_total": 2,
  "authors": [
    {
      "name": "Hongliang Lai"
    },
    {
      "name": "Bo Pang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7a2p5gvnt9zrz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13809",
  "fulltext_url": null,
  "id": "7a2p5gvnt9zrz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13809",
  "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": "W7213343865",
  "pdf_url": "https://arxiv.org/pdf/2609.13809",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7a2p5gvnt9zrz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13809",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13809"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Concept lattices of $Q$-relations via diagonal and back-diagonal categories",
  "title_text": "Concept lattices of Q-relations via diagonal and back-diagonal categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7a2p5gvnt9zrz",
  "venue": "arXiv",
  "versions": []
}