Foundations of Physics 43 (4):458-501 (2013)

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Abstract
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a causal category . We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics
Keywords Process  Causality  Symmetric monoidal categories  Quantum theory
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DOI 10.1007/s10701-012-9646-8
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Process and Reality.Arthur E. Murphy - 1931 - Journal of Philosophical Studies 6 (21):102-106.
Why John von Neumann Did Not Like the Hilbert Space Formalism of Quantum Mechanics (and What He Liked Instead).Miklos Rédei - 1996 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 27 (4):493-510.
Time, the Implicate Order and Pre-Space.David Bohm - 1986 - In David Ray Griffin (ed.), Physics and the Ultimate Significance of Time. State University of New York Press. pp. 172--208.

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