{
  "annotation_id": "3f5b0482-677a-4f2d-a499-23859de01b54",
  "date_created": "2026-03-02T18:01:45.967000Z",
  "date_modified": "2026-03-02T18:01:45.967000Z",
  "file_hash": "fe097d1ee3224ef1aa525ad692d4ebb8960c2747fc0db3399c05fa19f1cf5be9",
  "private": false,
  "record": {
    "abstract": "We show that the natural mathematical structure to describe a physical entity\nby means of its states and its properties within the Geneva-Brussels approach\nis that of a state property system. We prove that the category of state\nproperty systems (and morphisms), SP, is equivalent to the category of closure\nspaces (and continuous maps), Cls. We show the equivalence of the \u0027state\ndetermination axiom\u0027 for state property systems with the \u0027T0 separation axiom\u0027\nfor closure spaces. We also prove that the category SP0 of state determined\nstate property systems is equivalent to the category L0 of based complete\nlattices. In this sense the equivalence of SP and Cls generalizes the\nequivalence of Cls0 and L0, proven in Erne 1984.",
    "arxiv_id": "quant-ph/0105108",
    "authors": [
      "Diederik Aerts",
      "Eva Colebunders",
      "Ann Van der Voorde",
      "Bart Van Steirteghem"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "International Journal of Theoretical Physics, 38, 1999, 259",
    "title": "State property systems and closure spaces: a study of categorical   equivalence",
    "url": "https://arxiv.org/abs/quant-ph/0105108"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "acead3ed-86f1-4b7a-8c1b-baf340480198",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}