References

  1. Samson Abramsky & Adam Brandenburger (2011): A Unified Sheaf-Theoretic Account of Non-Locality and Contextuality. ArXiv:quant-ph/1102.0264v2.
  2. Bernhard Banaschewski & Christopher J. Mulvey (2006): A Globalisation of the Gelfand Duality Theorem. Annals of Pure and Applied Logic 137, pp. 62–103, doi:10.1016/j.apal.2005.05.018.
  3. Martijn Caspers, Chris Heunen, Nicolaas P. Landsman & Bas Spitters (2009): Intuitionistic Quantum Logic of an n-level System. Foundations of Physics 39, pp. 731–759, doi:10.1007/s10701-009-9308-7.
  4. Thierry Coquand & Bas Spitters (2009): Integrals and Valuations. Journal of Logic and Analysis 1(3), pp. 1–22, doi:10.4115/jla.2009.1.3.
  5. Andreas Döring (2009): Quantum States and Measures on the Spectral Presheaf. Advanced Science Letters 2(2), pp. 291–301.
  6. Andreas Döring & Chris Isham (2011): Classical and Quantum Probabilities as Truth Values. ArXiv:1102.2213.
  7. Andreas Döring & Chris Isham (2011): `What is a Thing?': Topos Theory in the Foundations of Physics. In: Bob Coecke: New Structures for Physics, chapter 13, Lecture Notes in Physics 813. Springer Verlag, Berlin Heidelberg, pp. 753–937, doi:10.1007/978-3-642-12821-9_13. ArXiv:0803.0417v1..
  8. M.P. Fourman & D.S. Scott (1979): Sheaves and Logic. In: M.P. Fourman, C.J. Mulvey & D.S. Scott: Applications of Sheaves, Lecture Notes in Mathematics 753. Springer-Verlag, pp. 302–401, doi:10.1007/BFb0061824.
  9. M. Giry (1981): A Categorical Approach to Probability Theory. In: Categorical Aspects of Topology and Analysis, Lecture Notes in Mathematics 915. Springer-Verlag, Berlin, pp. 68–85, doi:10.1007/s11225-010-9232-z.
  10. Reinhold Heckmann (1994): Probabilistic Power Domains, Information Systems, and Locales. In: Stephen Brookes, Michael Main, Austin Melton & David Schmidt: Mathematical Foundations in Programming Semantics – 9th International Conference, 1993, Lecture Notes in Computer Science 802. Springer, Berlin / Heidelberg, pp. 410–437.
  11. Chris Heunen, Nicolaas P. Landsman & Bas Spitters (2008): The Principle of General Tovariance. In: Rui Loja Fernandez & Roger Picken: Geometry and Physics, XVI International Fall Workshop, Lisbon, Portugal, 5-8 September 2007, AIP Conference Proceedings, Mathematical and Statistical Physics 1023. Springer.
  12. Chris Heunen, Nicolaas P. Landsman & Bas Spitters (2009): A Topos for Algebraic Quantum Theory. Communications in Mathematical Physics 291(1), pp. 63–110, doi:10.1007/s00220-009-0865-6.
  13. Chris Heunen, Nicolaas P. Landsman & Bas Spitters (2010): Bohrification of Operator Algebras and Quantum Logic. ArXiv:quant-ph/0905.2275v4.
  14. C.J. Isham & J. Butterfield (1998): Topos Perspectives on the Kochen-Specker Theorem I. Quantum States as Generalized Valuations. International Journal of Theoretical Physics 37(11), pp. 2669–2733, doi:10.1023/A:1026680806775.
  15. C.J. Isham & J. Butterfield (1999): Topos Perspectives on the Kochen-Specker Theorem II. Conceptual Aspects and Classical Analogues. International Journal of Theoretical Physics 38(3), pp. 827–859, doi:10.1023/A:1026652817988.
  16. P.T. Johnstone (1993): Fibrations and Partial Products in a 2-category. Applied Categorical Structures 1, pp. 141–179, doi:10.1007/BF00880041.
  17. C. Jones & G. Plotkin (1989): A Probabilistic Powerdomain of Evaluations. In: LICS '89. IEEE Computer Society Press, pp. 186–195.
  18. A. Joyal & M. Tierney (1984): An Extension of the Galois Theory of Grothendieck. Memoirs of the American Mathematical Society 309.
  19. Simon Kochen & Ernst Specker (1967): The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics 17, pp. 59–87.
  20. Bas Spitters (2010): The space of Measurement Outcomes as a Spectrum for Non-Commutative Algebras. In: S. Barry Cooper, Prakash Panangaden & Elham Kashefi: Proceedings Sixth Workshop on Developments in Computational Models: Causality, Computation, and Physics (DCM 2010), Electronic Proceedings in Theoretical Computer Science 26, pp. 127–134, doi:10.4204/EPTCS.26.12.
  21. Ross Street (1974): Fibrations and Yoneda's Lemma in a 2-category. In: G.M. Kelly: Category Seminar Sydney 1972/73, Lecture Notes in Mathematics 420, pp. 104–133.
  22. Steven Vickers (2008): A Localic Theory of Lower and Upper Integrals. Mathematical Logic Quarterly 54(1), pp. 109–123, doi:10.1002/malq.200710028.
  23. Steven Vickers (2011): Continuity is Geometricity. Talk given at workshop ``Logic, Categories, Semantics'' at Bordeaux, November 2010. Preprint at http://www.cs.bham.ac.uk/~sjv/GeoAspects.pdf.
  24. Steven Vickers (2011): A Monad of Valuation Locales. Preprint at http://www.cs.bham.ac.uk/~sjv/Riesz.pdf.

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