Hopf algebras and linear logic

Mathematical Structures in Computer Science

Volumn 6, Issue 2, 1996, Pages 189-217

  Blute, Richard F ^a  

^a UNIVERSITY OF OTTAWA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR ALGEBRA; TENSORS; TOPOLOGY; VECTOR SPACES;

AUTONOMOUS CATEGORIES; CLASSICAL LINEAR LOGIC; MONOIDAL CATEGORIES; MONOIDAL CLOSED STRUCTURES; NON-COMMUTATIVE LOGIC; TOPOLOGICAL CATEGORY; TOPOLOGICAL STRUCTURE; TOPOLOGICAL VECTOR SPACES;

ALGEBRA;

EID: 0000281126     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129500000943     Document Type: Article

References (50)

1. Abe, K. (1977) Hopf Algebras, Cambridge University Press.
2. Abramsky, S. and Jagadeesan, R. (1992) Games and Full Completeness for Linear Logic (preprint).
3. Abrusci, V. M. (1991) Phase Semantics and Sequent Calculus for Pure Noncommutative Classical Linear Propositional Logic. Journal of Symbolic Logic 56 1403-1451.
4. Abrusci, V. M. (1993) Talk given at Linear Logic Conference, Cornell University.
5. Barr, M. (1976a) Duality of Vector Spaces. Cahiers de Top. et Geom. Diff. 17 3-14.
6. Barr, M. (1976b) Duality of Banach Spaces. Cahiers de Top. et Geom. Diff. 17 15-32.
7. Barr, M. (1976c) Closed Categories and Topological Vector Spaces. Cahiers de Top. et Geom. Diff. 17 223-234.
8. Barr, M. (1976d) Closed Categories and Banach Spaces. Cahiers de Top. et Geom. Diff. 17 335-342.
9. Barr, M. (1979) "Autonomous Categories. Springer-Verlag Lecture Notes in Mathematics 752.
10. Barr, M. (1994) Nonsymmetric ∗-Autonomous Categories. To appear in Theoretical Computer Science.
11. Barr, M. (1995) '-autonomous Categories Revisited. To appear in Journal of Pure and Applied Algebra.
12. Benabou, J. (1963) Categories avec Multiplication. C.R. Acad. Sci. Paris 256 1887-1890
13. Benson, D. B. (1989) Bialgebras: Some Foundations for Distributed and Concurrent Computation. Fundamenta Informaticae 12 427-486.
14. Blute, R. (1993) Linear Logic, Coherence and Dinaturality. Theoretical Computer Science 115 3-41.
15. Blute, R. (1995) Braided Proof Nets and Categories (in preparation).
16. Blute, R., Cockett, J. R. B., Seely, R. A. G. and Trimble, T. (1995) Natural Deduction and Coherence for Weakly Distributive Categories. To appear in Journal of Pure and Applied Algebra.
17. Deligne, P. and Milne, J. (1982) Tannakian Categories. Springer-Verlag Lecture Notes in Mathematics 900.
18. Drinfel'd, V. G. (1986) Quantum Groups. Proceedings of the International Congress of Mathematicians 798-820.
19. Eilenberg, S. and Kelly, G. M. (1966) Closed Categories. In: Proceedings of the International Conference on Categroical Algebra, Springer-Verlag.
20. Fleury, A. and Retore, C. (1994) The MIX Rule. Mathematical Structures in Computer Science 4 273-285.
21. Fulton, W. and Harris, J. (1991) Representation Theory. Springer-Verlag Graduate Texts in Mathematics 129.
22. Geroch, R. (1985) Mathematical Physics, University of Chicago Press.
23. Gerstenhaber, M., Giaquinto, A. and Schack, D. (1992) Quantum Symmetry. Springer-Verlag Lecture Notes in Mathematics 1510.
24. Girard, J. Y. (1987) Linear Logic. Theoretical Computer Science 50 1-102.
25. Gonthier, G., Abadi, M. and Levy, J. J. (1992) Linear Logic Without Boxes. In: Proceedings of Logic in Computer Science, IEEE.
26. Joni, S. and Rota, G. (1979) Coalgebras and Bialgebras in Combinatorics. Studies in Applied Mathematics 61 93-139.
27. Joyal, A. and Street, R. (1991) An Introduction to Tannaka Duality and Quantum Groups. Springer- Verlag Lecture Notes in Mathematics 1488.
28. Joyal, A. and Street, R. (1992) Braided Tensor Categories. To appear in Advances in Mathematics.
29. Kelly, G. M. (1972) An Abstract Approach to Coherence. Springer-Verlag Lecture Notes in Mathematics 281.
30. Kelly, G. M. and La Plaza, M. (1980) Coherence for Compact Closed Categories. Journal of Pure and Applied Algebra 19 193-213.
31. Kelly, G. M. and Mac Lane, S. (1971) Coherence for Closed Categories. Journal of Pure and Applied Algebra 1 97-140.
32. Lambek, J. (1969) Deductive Systems and Categories II. Springer-Verlag Lecture Notes in Mathematics 87.
33. Lambek, J. (1993) Bilinear Logic in Algebra and Linguistics (preprint).
34. Lambek, J. and Scott, P. (1986) Introduction to Higher Order Categorical Logic, Cambridge University Press.
35. Lefschetz, S. (1963) Algebraic Topology. American Mathematical Society Colloquium Publications 27.
36. Mac Lane, S. (1963) Natural Associativity and Commutativity. Rice University Studies 49 28-46.
37. Majid, S. (1990a) Physics for Algebraists: Noncommutative and Noncocommutative Hopf Algebras by a Bicrossproduct Construction. J. of Alg. 130 17-64.
38. Majid, S. (1990b) Quasitriangular Hopf Algebras and Yang-Baxter Equations. International Journal of Modern Physics 5 1-91.
39. Majid, S. (1992) Tannaka-Krein Theorem for Quasihopf Algebras and Other Results. Proceedings of the Conference on Deformation Theory and Quantum Groups. Contemporary Mathematics 134.
40. Majid, S. (1993) Braided Groups. Journal of Pure and Applied Algebra 86 187-221.
41. Makkai, M. (1987) Stone Duality for First Order Logic. Advances in Mathematics 65 97-170.
42. Rosen thai, K. I. (1990) A Note on Girard Quantales. Cahiers Top. Geom. Diff. 31 3-12.
43. Saavedra-Rivano, R. (1972) Categories Tannakiennes. Springer-Verlag Lecture Notes in Mathematics 265.
44. Schmitt, W. (1987) Antipodes and Incidence Coalgebras. Journal of Combinatorial Theory 46 264-290.
45. Scott, D. (1972) Continuous Lattices. Springer-Verlag Lecture Notes in Mathematics 274.
46. Seely, R. A. G. (1989) Linear Logic, -Autonomous Categories and Cofree Coalgebras. In: Categories in Computer Science and Logic. Contemporary Mathematics 92, AMS.
47. Sweedler, M. (1969) Hopf Algebras, Benjamin Press.
48. Ulbrich, K. (1989) On Hopf Algebras and Rigid Monoidal Categories. Isr. J. of Math. 71 252-256.
49. Willard, S. (1970) General Topology, Addison-Wesley.
50. Yetter, D. (1990) Quantales and (noncommutative) Linear Logic. Journal of Symbolic Logic 55 41-64