A Topos Foundation for Theories of Physics: IV. Categories of Systems

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dc.creatorDoering, A.
dc.creatorIsham, C. J.
dc.date2007-03-07
dc.date.accessioned2026-07-07T12:00:30Z
dc.date.available2026-07-07T12:00:30Z
dc.descriptionThis paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. The previous papers in this series are concerned with implementing this programme for a single system. In the present paper, we turn to considering a collection of systems: in particular, we are interested in the relation between the topos representation for a composite system, and the representations for its constituents. We also study this problem for the disjoint sum of two systems. Our approach to these matters is to construct a category of systems and to find a topos representation of the entire category.
dc.description38 pages, no figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0703066
dc.identifierhttp://arxiv.org/abs/quant-ph/0703066
dc.identifierJ.Math.Phys.49:053518,2008
dc.identifierdoi:10.1063/1.2883826
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/206858
dc.subjectQuantum Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.titleA Topos Foundation for Theories of Physics: IV. Categories of Systems
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