{
  "annotation_id": "dfea3134-6a82-48ae-9aec-ff9a9ae92971",
  "date_created": "2026-03-02T18:02:34.694000Z",
  "date_modified": "2026-03-02T18:02:34.694000Z",
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  "record": {
    "abstract": "This paper is the fourth in a series whose goal is to develop a fundamentally\nnew way of building theories of physics. The motivation comes from a desire to\naddress certain deep issues that arise in the quantum theory of gravity. Our\nbasic contention is that constructing a theory of physics is equivalent to\nfinding a representation in a topos of a certain formal language that is\nattached to the system. Classical physics arises when the topos is the category\nof sets. Other types of theory employ a different topos. The previous papers in\nthis series are concerned with implementing this programme for a single system.\nIn the present paper, we turn to considering a collection of systems: in\nparticular, we are interested in the relation between the topos representation\nfor a composite system, and the representations for its constituents. We also\nstudy this problem for the disjoint sum of two systems. Our approach to these\nmatters is to construct a category of systems and to find a topos\nrepresentation of the entire category.",
    "arxiv_id": "quant-ph/0703066",
    "authors": [
      "A. Doering",
      "C. J. Isham"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.2883826",
    "journal_ref": "J.Math.Phys.49:053518,2008",
    "title": "A Topos Foundation for Theories of Physics: IV. Categories of Systems",
    "url": "https://arxiv.org/abs/quant-ph/0703066"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
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    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}