Abstract scalars, loops, and free traced and strongly compact closed categories

Lecture Notes in Computer Science

Volumn 3629, Issue , 2005, Pages 1-29

  Abramsky, Samson ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DATA STRUCTURES; QUANTUM THEORY; THEOREM PROVING;

ABSTRACT SCALARS; CLOSED CATEGORY; FREE CONSTRUCTION; PHYSICAL THEORY;

ABSTRACTING;

EID: 26944485450     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11548133_1     Document Type: Conference Paper

References (25)

1. S. Abramsky, R. Jagadeesan, New Foundations for the Geometry of Interaction, Information and Computation, 111(1):53-119, 1994. Conference version appeared in LiCS '92.
2. S. Abramsky. Retracing some paths in process algebra. CONCUR 96: Proceedings of the Seventh International Conference on Concurrency Theory, LNCS 1119, 1-17, 1996.
3. S. Abramsky and E. Haghverdi and P. J. Scott. Geometry of Interaction and Linear Combinatory Algebras. Mathematical Structures in Computer Science 12:625-665, 2002.
4. S. Abramsky and B. Coecke. A categorical semantics of quantum protocols. Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LiCS'04), IEEE Computer Science Press, 415-425, 2004. (extended version at arXiv: quant-ph/0402130)
5. S. Abramsky and B. Coecke. Abstract Physical Traces. Theory and Applications of Categories, 14:111-124, 2005.
6. S. Abramsky and R. W. Duncan. Categorical Quantum Logic. In the Proceedings of the Second International Workshop on Quantum Programming Languages, 2004.
7. M. Barr. *-autonomous Categories. Springer-Verlag 1979.
8. G. Birkhoff and J. von Neumann. The logic of quantum mechanics. Annals of Mathematics 37, 823-843, 1937.
9. B. Coecke. Delinearizing Linearity. Draft paper, 2005.
10. P. Deligne. Catégories Tannakiennes. In The Grothendiek Festschrift, Vol. II, 111-195. Birkhauser 1990.
11. J.-Y. Girard, Linear Logic. Theoretical Computer Science 50(1):1-102, 1987.
12. J.-Y. Girard, Geometry of Interaction I: Interpretation of System F, in: Logic Colloquium '88, ed. R. Ferro, et al. North-Holland, pp. 221-260, 1989.
13. Martin Hyland. Personal communication, July 2004.
14. A. Joyal, R. Street and D. Verity, Traced monoidal categories. Math. Proc. Camb. Phil. Soc. 119, 447-468, 1996.
15. C. Kassel. Quantum Groups. Springer-Verlag 1995.
16. P. Katis, N. Sabadini and R. F. C. Walters. Feedback, trace and fixed point semantics. Proceedings of FICS01: Workshop on Fixed Points in Computer Science, 2001. Available at http://www.unico.it/ walters/papers/index.html
17. G. M. Kelly. Many-variable functorial calculus I. Springer Lecture Notes in Mathematics 281, 66-105, 1972.
18. G. M. Kelly. An abstract approach to coherence. Springer Lecture Notes in Mathematics 281, 106-147, 1972.
19. G. M. Kelly and M. L. Laplaza. Coherence for compact closed categories. Journal of Pure and Applied Algebra 19, 193-213, 1980.
20. S. Mac Lane. Categories for the Working Mathematician. Springer-Verlag 1971.
21. Dusko Pavlovic. A semantical approach to equilibria, adaptation and evolution. Unpublished manuscript, November 2004.
22. R. Penrose. Applications of negative-dimensional tensors. In Combinatorial Mathematics and Its Applications, ed. D. J. Welsh, 221-244, Academic Press 1971.
23. N. S. Rivano. Catégories Tannakiennes. Springer-Verlag 1972.
24. P. Selinger. Towards a quantum programming language. Mathematical Structures in Computer Science 14(4), 527-586, 2004.
25. P. Selinger. Dagger compact closed categories and completely positive maps. To appear in Proceedings of the 3rd International Workshop on Quantum Programming Languages, 2005.