Abstract
We take a first step towards establishing a link between the topos approach to quantum theory and the monoidal approach to quantum theory. The topos approach to quantum theory makes extensive use of categories of commutative \(C^*\)-algebras and their corresponding Gelfand spectrum. We generalise these categories of \(C^*\)-algebras and generalise the notion of Gelfand spectrum via defining the abstract spectral presheaf. We then characterise this spectral presheaf for the category of sets and relations, and examine how this relates to the notion of observable in this category as studied in the monoidal approach to quantum theory.
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Dunne, K. (2017). A New Perspective on Observables in the Category of Relations: A Spectral Presheaf for Relations. In: de Barros, J., Coecke, B., Pothos, E. (eds) Quantum Interaction. QI 2016. Lecture Notes in Computer Science(), vol 10106. Springer, Cham. https://doi.org/10.1007/978-3-319-52289-0_20
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DOI: https://doi.org/10.1007/978-3-319-52289-0_20
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