Differential categories

Mathematical Structures in Computer Science

Volumn 16, Issue 6, 2006, Pages 1049-1083

  Blute, R F ^a   Cockett, J R B ^b   Seely, R A G ^c  

^a UNIVERSITY OF OTTAWA   (Canada)

^b UNIVERSITY OF CALGARY   (Canada)

^c MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845603943     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129506005676     Document Type: Article

References (25)

1. Barr, M. B. (1979) *-Autonomous Categories. Springer-Verlag Lecture Notes in Mathematics 752.
2. Bespalov, Y. and Drabant, B. (1997) Differential Calculus in Braided Abelian Categories. (Preprint, available at http://arxiv.org/abs/q-alg/9703036.)
3. Bierman, G. (1995) What is a categorical model of intuitionistic linear logic? In: Proceedings of the Second International Conference on Typed Lambda Calculus and Applications, Edinburgh, Scotland. Springer-Verlag Lecture Notes in Computer Science 902 73-93.
4. Blute, R. F., Cockett, J. R. B. and Seely, R. A. G. (1996) ! and ? : Storage as tensorial strength. Mathematical Structures in Computer Science 6 313-351.
5. Blute, R. F., Cockett, J. R. B. and Seely, R. A. G. (2006) Cartesian differential categories (in preparation).
6. Blute, R. F., Cockett, J. R. B., Seely, R. A. G. and Trimble, T. (1997) Natural deduction and coherence for weakly distributive categories. Journal of Pure and Applied Algebra 113 229-296.
7. Cockett, J. R. B. (1993) Introduction to distributive categories. Mathematical Structures in Computer Science 3 277-308.
8. Ehresmann, C. (1959) Catégories topologiques et catégories différentiables. In: Coll. Géom. Diff. Globale (Bruxelles, 1958), Centre Belge Rech. Math. Louvain 137-150.
9. Ehresmann, C. (1980-1983) Charles Ehresmann: Oeuvres complètes et commentées. Edited by A. C. Ehresmann and published as supplements to Cahiers de Topologie et Géométrie Différentielle, Amien 21-24.
10. Ehrhard, T. (2001) On Köthe sequence spaces and linear logic. Mathematical Structures in Computer Science 12 579-623.
11. Ehrhard, T. (2005) Finiteness spaces. Mathematical Structures in Computer Science 15 615-646.
12. Ehrhard, T. and Regnier, L. (2003) The differential λ-calculus. Theoretical Computer Science 309 (1-3) 1-41.
13. Ehrhard, T. and Regnier, L. (2005) Differential interaction nets. Invited paper for Workshop on Logic, Language, Information and Computation (WoLLIC). Electronic Notes in Theoretical Computer Science 123.
14. Frolicher, A. and Kriegl, A. (1988) Linear Spaces and Differentiation Theory, Wiley Publishing.
15. Girard, J.-Y. (1987) Linear Logic. Theoretical Computer Science 50 1-102.
16. Hyland, M. and Schalk, A. (2003) Glueing and Orthogonality for Models of Linear Logic. Theoretical Computer Science 294 183-231.
17. Iglesias-Zemmour, P. (2006) Introduction to Diffeology. (Online textbook available at http://www.umpa.ens-lyon.fr/~iglesias.)
18. Kassel, C. (1995) Quantum Groups, Graduate Texts in Mathematics 155, Springer-Verlag.
19. Lang, S. (2002) Algebra, Graduate Texts in Mathematics, Springer-Verlag.
20. Mac Lane, S. (1971) Categories for the Working Mathematician, Graduate Texts in Mathematics, Springer-Verlag.
21. Majid, S. (1993) Free Braided Differential Calculus, Braided Binomial Theorem and the Braided Exponential Map. Journal of Mathematical Physics 34 4843-4856.
22. Manes, E. G. (1976) Algebraic Theories, Graduate Texts in Mathematics 26, Springer Verlag.
23. Schalk, A. (2004) What is a categorical model of linear logic? (Course notes.)
24. Seely, R. A. G. (1989) Linear logic, *-autonomous categories and cofree coalgebras. In: Gray, J. and Scedrov, A. (eds.) Categories in Computer Science and Logic. Contemporary Mathematics 92.
25. Woronowicz, S. L. (1989) Differential calculus on compact matrix pseudogroups (quantum groups). Comm. Math. Phys. 122 125-170.