{
  "annotation_id": "e931dca0-bdfa-44f2-af34-382fef46758c",
  "date_created": "2026-02-17T05:53:11.939000Z",
  "date_modified": "2026-02-17T05:53:11.939000Z",
  "file_hash": "c3bc64837243111d55de7a8e8f10de028b0a31076f631f513192675f6212ece8",
  "private": false,
  "record": {
    "abstract": "In operator-algebraic AQFT one routinely moves back and forth between two kinds of structure: inclusions of local algebras coming from inclusions of regions, and bimodules/intertwiners that implement the standard $L^2$-based constructions used to compare and compose observables. The obstruction to making this interplay genuinely functorial is that there are two independent compositions (restriction along inclusions and fusion/transport along bimodules) and they must be compatible on commuting spacetime diagrams, which is exactly the situation a double category is designed to encode. Part I resolves this by building a spacetime double category and a von Neumann algebra double category inspired by previous work by Orendain, and by packaging an AQFT input as a pseudo double functor whose vertical part is the Haag-Kastler net and whose squares record the required compatibilities in a well-typed way forced by commutativity. We formulate the Haag-Kastler axioms in this setup, establish the coherence needed for the construction, and work out representative examples.",
    "arxiv_id": "2601.07807",
    "authors": [
      "Khyathi Komalan"
    ],
    "categories": [
      "math.CT",
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Double Categorical Approaches to AQFT I: Axiomatic Setup",
    "url": "https://arxiv.org/abs/2601.07807",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b5c5c204-4d54-49e3-830a-d6105e89d12b",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}