{
  "abstract": "We study first-order locally convex Lie algebroids in the setting of Bastiani calculus. The first-order condition is automatic in finite rank, but is an additional regularity hypothesis for general locally convex vector bundles. We define sheaves of scalar-valued and vector-valued Lie algebroid forms as fiberwise continuous alternating maps with smooth local representatives. Morphisms are defined by requiring the induced pullback on inverse-image sheaves of scalar-valued forms to commute with the Lie algebroid differentials. We prove that these algebroids form a category, study representations and cohomology sheaves, and show that the Lie algebroids and morphisms of locally convex Lie groupoids belong to this category. We also give two applications. For a compact manifold $K$, the current algebroid $C^\\infty(K,A)\\to C^\\infty(K,M)$ of a first-order Banach Lie algebroid $A\\to M$ is a first-order Fréchet Lie algebroid, provided $M$ admits local addition. Finally, we prove a Banach Lie II theorem: a morphism from the Lie algebroid of a locally convex Lie groupoid to that of a Banach-Lie groupoid, both with Hausdorff source fibers, integrates uniquely to a groupoid morphism when the source groupoid is source-connected and source-simply connected.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.07672",
  "author_total": 1,
  "authors": [
    {
      "name": "Ahmed Gamal Shaltut"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kb6v9bfypxse.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.07672",
  "fulltext_url": null,
  "id": "6kb6v9bfypxse",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.07672",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7167812769",
  "pdf_url": "https://arxiv.org/pdf/2607.07672",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kb6v9bfypxse.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2607.07672",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.07672"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A category of locally convex Lie algebroids",
  "title_text": "A category of locally convex Lie algebroids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/6kb6v9bfypxse",
  "venue": "arXiv",
  "versions": []
}