{
  "abstract": "We develop a functorial framework for ample C$^*$-diagonal pairs and their Weyl groupoids. The main contribution is a partial functoriality theorem in the untwisted setting: from a diagonal-preserving $*$-homomorphism whose restriction to the diagonal is an isomorphism, we construct an open subgroupoid $\\mathcal H_Φ\\subseteq\\mathcal G_B$ and a continuous, open, injective groupoid homomorphism $ρ_Φ: \\mathcal H_Φ\\to\\mathcal G_A$, together with the induced homeomorphism on unit spaces. We prove that this construction is well-defined and extends to a contravariant functor into a category of partial groupoid morphisms, thereby giving a concrete partial Weyl-groupoid functor. We record consequences for expectation-compatible ideals, faithful conditional expectations, and quotient reductions, and formulate questions concerning the interaction with dynamical comparison. We also record tensor-product permanence results, including the product description of Weyl groupoids and the relevant diagonal-dimension estimate. Finally, in the untwisted principal case, we prove a reconstruction/rigidity theorem showing that the underlying Weyl groupoid determines the diagonal pair up to isomorphism. Results imported from Bönicke--Li, Li--Liao--Winter, Renault, Kumjian, and Kopsacheilis--Winter are used explicitly as background or supporting permanence results rather than claimed as new contributions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.25627",
  "author_total": 1,
  "authors": [
    {
      "name": "Ali Jabbari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9hgmfbepe840a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.25627",
  "fulltext_url": null,
  "id": "9hgmfbepe840a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.25627",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7162450042",
  "pdf_url": "https://arxiv.org/pdf/2605.25627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9hgmfbepe840a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2605.25627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.25627"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Functoriality and Weyl Groupoids of Ample C*-Diagonal Pairs",
  "title_text": "Functoriality and Weyl Groupoids of Ample C*-Diagonal Pairs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9hgmfbepe840a",
  "venue": "arXiv",
  "versions": []
}