Operational resolutions and state transitions in a categorical setting

Foundations of Physics Letters

Volumn 12, Issue 1, 1999, Pages 29-49

  Coecke, Bob ^a   Stubbe, Isar ^b  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Closure space; Complete lattice; Quantales and quantaloids; State and property transitions

Indexed keywords

EID: 0041494423     PISSN: 08949875     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021626704772     Document Type: Article

References (32)

1. J. Adamek, H. Herrlich, and G. E. Strecker, Abstract and Concrete Categories (Wiley, New York, 1990).
2. D. Aerts, Found. Phys. 24, 1227 (1982).
3. H. Amira, B. Coecke and I. Stubbe, Helvetica Phys. Acta 71, 554 (1998).
4. G. Birkhoff, Lattice Theory, AMS Coll. Publ. (1940).
5. F. Borceux, Handbook of Categorical Algebra Part 1 and 2 (Cambridge University Press, Cambridge, 1994).
6. B. Coecke, Helvetica Phys. Acta 68, 394 (1995).
7. B. Coecke, Found. Phys. 28, 1109 (1998).
8. B. Coecke, Found. Phys. 28, 1347 (1998).
9. B. Coecke, "Structural characterization of compoundness," submitted to Int. J. Theor. Phys., for the proceedings of IQSA-Liptovski Jan 1998 (n.d.).
10. B. Coecke and S. Smets, "A logical description for perfect measurements," submitted to Int. J. Theor. Phys., for the proceedings of IQSA-Liptovski Jan 1998 (n.d.).
11. B. Coecke and I. Stubbe, "On a duality of quantales emerging from an operational resolution," to appear in Int. J. Theor. Phys., for the proceedings of IQSA, Atlanta, 1997 (1999).
12. W. Daniel, Helvetica Phys. Acta 62, 941 (1989).
13. D. J. Foulis, Proc. AMS 11, 648 (1960).
14. Cl.-A. Faure and A. Frölicher, Geom. Dedicata 47, 25 (1993).
15. Cl.-A. Faure, D.J. Moore and C. Piron, Helvetica Phys. Acta 68, 150 (1995).
16. J.Y. Girard, Theor. Comp. Sc. 50 (1987).
17. P.T. Johnstone, Stone Spaces (Cambridge University Press, Cambridge, 1982).
18. A. Joyal and M. Tierney, Mem. AMS 51, No.309 (1984).
19. S. MacLane, Categories for the Working Mathematician (Springer, New York, 1971/1997).
20. D. J. Moore, Helvetica Phys. Acta 68, 658 (1995).
21. D. J. Moore, Int. J. Theor. Phys. 36, 2211 (1997).
22. C. J. Mulvey, Rend. Circ. Math. Palermo 12, 99 (1986).
23. C. J. Mulvey and J. Wick-Pelletier, Canadian Math. Soc. Conf. Proc. 13, 345 (1992).
24. J. Paseka, "Simple Quantales," P. Simon, ed., Proceedings, 8th Prague Topology Symposium, p. 314 (1996).
25. C. Piron, Helvetica Phys. Acta 37, 439 (1964).
26. C. Piron, Foundations of Quantum Physics (Benjamin, New York, 1976).
27. C. Piron, J. Phyl. Logic 6, 481 (1977).
28. A. M. Pitts, Proc. London Math. Soc. 57, 433 (1988).
29. J .C. T. Pool, Comm. Math. Phys. 9, 118 (1968).
30. K. I. Rosenthal, Quantales and Their Applications, Pitmann Research Notes in Math. 234, Longmann Sc. & Tech. Publ. (1990).
31. K. I. Rosenthal, J. Pure Appl. Alg. 77, 67 (1991).
32. D. N. Yetter, J. Symb. Logic 55, 41 (1990).