{
  "abstract": "It is part of the folklore of category theory that every *-autonomous category is a linearly distributive category, but a full proof, with all coherence conditions verified, is not available in the literature. We give such a proof. The key observation is that the linear distributions, and the coherences they must satisfy, are strengths and strength coherences for the internal-hom functors of a biclosed monoidal category, arising from the correspondence between enrichments and strengths. Working with an arbitrary biclosed monoidal category V, we construct a canonical cotensor product on V , show that the two candidate linear distributions are composed strengths satisfying the interchange and dual interchange coherences, and that (V, \\par, 0, α , λ , ρ ) is a skew monoidal category in the sense of Szlachányi and of Uustalu, Veltri and Zeilberger. When V is *-autonomous, the skew monoidal structure upgrades to a genuine monoidal structure, and we obtain that every *-autonomous category is a planar linearly distributive category, with no symmetry of ⊗ or cyclicity of the dualizing object required.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Gregory Chichery"
    },
    {
      "name": "Luigi Santocanale"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23cmqj8vh91h7.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "23cmqj8vh91h7",
  "issns": [],
  "landing_url": "https://hal.science/hal-05770015v1",
  "language": "en",
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.info.info-lo"
    ],
    [
      "hal",
      "1.math.math-ct"
    ],
    [
      "hal",
      "1.math.math-lo"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05770015/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23cmqj8vh91h7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05770015",
      "source": "hal",
      "url": "https://hal.science/hal-05770015v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ct",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-lo",
      "subfield": "logic-foundations"
    }
  ],
  "title": "From *-Autonomous to Linearly Distributive via Enrichments and Strengths",
  "title_text": "From *-Autonomous to Linearly Distributive via Enrichments and Strengths",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/23cmqj8vh91h7",
  "venue": "HAL",
  "versions": []
}