Entropic Hopf algebras and models of non-commutative logic

Theory and Applications of Categories

Volumn 10, Issue 1, 2002, Pages 424-460

  Blute, Richard F ^a   Lamarche, François ^a   Ruet, Paul ^a  

^a NONE

Author keywords

Hopf algebras; Linear logic; Monoidal categories

Indexed keywords

EID: 18444394583     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. E. Abe. Hopf algebras. Cambridge University Press, 1980.
2. V. M. Abrusci and P. Ruet. Non-commutative logic I: the multiplicative fragment. Annals Pure Appl. Logic, 101(1):29-64, 2000.
3. M. Barr. *-autonomous categories. Springer LNM, 752, 1979.
4. M. Barr. Non-symmetric *-autonomous categories. Theoret. Comp. Sci., 139:115-130, 1995.
5. M. Barr. The Chu construction. Theory Appl. Cat., 2:17-35, 1996.
6. R. Blute. Hopf algebras and linear logic. Math. Struct. in Comp. Sci., 6:189-217, 1996.
7. R. Blute, R. Cockett, and R. Seely. The logic of linear functors. To appear in Math. Struct. in Comp. Sci., 2002.
8. R. Blute and P. J. Scott. Linear Läuchli semantics. Annals Pure Appl. Logic, 77:101-142, 1996.
9. R. Blute and P. J. Scott. The shuffle Hopf algebra and noncommutative full completeness. J. Symb. Logic, 63 (4):1413-1436, 1998.
10. H. Cartan and S. Eilenberg. Homological Algebra. Princeton University Press, 1956.
11. J. R. B. Cockett, J. Koslowski, and R. A. G. Seely. Introduction to linear bicategories. Math. Struct. in Comp. Sci., 10(2), 2000.
12. B. J. Day. On closed categories of functors. In S. MacLane, editor, Reports of the Midwest Category Seminar. Springer LNM 137, 1970.
13. P. Deligne and J. Milne. Tannakian categories. Springer LNM, 900:101-228, 1982.
14. T. F. Fox. An introduction to algebraic deformation theory. J. Pure Appl. Algebra, 84, 1993.
15. P. Freyd. Abelian Categories. Harper and Row, 1964.
16. M. Gerstenhaber and S. D. Schack. Algebraic cohomology and deformation theory. In: Deformation Theory of Algebras and Structures and Applications, pages 11-264, 1988.
17. J.-Y. Girard. Linear logic. Theoret. Comp. Sci., 50(1):1-102, 1987.
18. A. Joyal. Une théorie combinatoire des séries formelles. Adv. Math., 42:1-82, 1981.
19. Ch. Kassel. Quantum groups. Graduate Texts in Mathematics 155. Springer, 1995.
20. G. M. Kelly and M. L. Laplaza. Coherence for compact closed categories. J. Pure Appl. Algebra, 19:193-213, 1980.
21. F. Lamarche. On the algebra of structural contexts. Submitted, 2002. Available at http://www.loria.fr/~lamarche.
22. J. Lambek. The mathematics of sentence structure. Amer. Math. Monthly, 65(3):154-170, 1958.
23. J. Lambek. Bilinear logic in algebra and linguistics. In J.Y. Girard, Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, volume 222 of London Math. Soc. Lec. Notes, page 43. Cambridge University Press, 1994.
24. S. Majid. Quasitriangular Hopf algebras and Yang-Baxter equations. Int. J. of Modern Physics, 5:1-91, 1990.
25. S. Majid. Foundations of quantum group theory. Cambridge University Press, 1995.
26. N. Saavedra Rivano. Catégories tannakiennes. Springer Lecture Notes in Mathematics, 265, 1972.
27. K. Rosenthal. *-autonomous categories of bimodules. J. Pure and App. Algebra, 97(2):189-202, 1994.
28. P. Ruet. Non-commutative logic II: sequent calculus and phase semantics. Math. Struct. in Comp. Sci., 10(2):277-312, 2000.
29. M. Sweedler. Hopf algebras. W. A. Benjamin, 1969.
30. K.H. Ulbrich. On Hopf algebras and rigid monoidal categories. Israel J. of Math., 72:252-256, 1990.
31. D.N. Yetter. Quantales and (non-commutative) linear logic. J. Symb. Logic, 55(1), 1990.