Involutive Categories and Monoids, with a GNS-Correspondence

Foundations of Physics

Volumn 42, Issue 7, 2012, Pages 874-895

  Jacobs, Bart ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Gelfand Naimark Segal; Inner products; Involution; Monoidal category

Indexed keywords

EID: 84861592164     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10701-011-9595-7     Document Type: Article

References (25)

1. Abramsky, S., Blute, R., Panangaden, P.: Nuclear and trace ideals in tensored *-categories. J. Pure Appl. Algebra 143, 3-47 (2000).
2. Abramsky, S., Coecke, B.: A categorical semantics of quantum protocols. In: Engesser, K., Gabbai, D. M., Lehmann, D. (eds.) Handbook of Quantum Logic and Quantum Structures, pp. 261-323. North Holland/Elsevier/Computer Science, Amsterdam (2009).
3. Arveson, W.: A Short Course on Spectral Theory. Springer, Berlin (2002).
4. Awodey, S.: Category Theory. Oxford Logic Guides. Oxford Univ. Press, London (2006).
5. Baez, J. C., Dolan, J.: Higher dimensional algebra III: n-categories and the algebra of opetopes. Adv. Math. 135, 145-206 (1998).
6. Barr, M., Wells, Ch.: Toposes, Triples and Theories. Springer, Berlin (1985). Revised and corrected version available from URL: www. cwru. edu/artsci/math/wells/pub/ttt. html.
7. Beggs, E. J., Majid, S.: Bar categories and star operations. Algebr. Represent. Theory 12, 103-152 (2009).
8. Blackwell, R., Kelly, G. M., Power, A. J.: Two-dimensional monad theory. J. Pure Appl. Algebra 59, 1-41 (1989).
9. Blute, R., Panangaden, P.: Dagger categories and formal distributions. In: Coecke, B. (ed.) New Structures in Physics. Lect. Notes Physics, vol. 813, pp. 421-436. Springer, Berlin (2010).
10. Borceux, F.: Handbook of Categorical Algebra. Encyclopedia of Mathematics, vols. 50-52. Cambridge Univ. Press, Cambridge (1994).
11. Coumans, D., Jacobs, B.: Scalars, monads and categories (2010). arXiv: 1003. 0585.
12. Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer Acad. Publ., Dordrecht (2000).
13. Egger, J. M.: Involutive monoidal categories (2010). Available via http://homepages. inf. ed. ac. uk/jegger.
14. Hasuo, I.: Tracing anonymity with coalgebras. PhD thesis, Radboud Univ. Nijmegen (2010).
15. Hasuo, I., Heunen, C., Jacobs, B., Sokolova, A.: Coalgebraic components in a many-sorted microcosm. In: Kurz, A., Tarlecki, A. (eds.) Conference on Algebra and Coalgebra in Computer Science (CALCO 2009). Lect. Notes Comp. Sci., vol. 5728, pp. 64-80. Springer, Berlin (2009).
16. Hasuo, I., Jacobs, B., Sokolova, A.: The microcosm principle and concurrency in coalgebra. In: Amadio, R. (ed.) Foundations of Software Science and Computation Structures. LNCS, vol. 4962, pp. 246-260. Springer, Berlin (2008).
17. Jacobs, B.: Categorical Logic and Type Theory. North Holland, Amsterdam (1999).
18. Jacobs, B.: Coalgebraic walks in quantum and Turing computation. In: Hofmann, M. (ed.) Foundations of Software Science and Computation Structures. Lect. Notes Comp. Sci., vol. 6604, pp. 12-26. Springer, Berlin (2011).
19. Jacobs, B.: Dagger categories of tame relations (2011). arXiv: 1101. 1077.
20. Kalmbach, G.: Orthomodular Lattices. Academic Press, London (1983).
21. Kock, A.: Bilinearity and cartesian closed monads. Math. Scand. 29, 161-174 (1971).
22. Kock, A.: Closed categories generated by commutative monads. J. Aust. Math. Soc. XII, 405-424 (1971).
23. Manes, E. G.: Algebraic Theories. Springer, Berlin (1974).
24. Mac Lane, S.: Categories for the Working Mathematician. Springer, Berlin (1971).
25. Street, R.: The formal theory of monads. J. Pure Appl. Algebra 2, 149-169 (1972).