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*-Autonomous categories and linear logic

Published online by Cambridge University Press:  04 March 2009

Michael Barr
Michael Barr
Affiliation:
Department of Mathematics and Statistics, MCGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
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Extract

The subject of linear logic has recently become very important in theoretical computer science. It is apparent that the *-autonomous categories studied at length in by Barr (1979) are a model for a large fragment of linear logic, although not quite for the whole thing. Since the main reference is out of print and since large parts of that volume are devoted to results highly peripheral to the matter at hand, it seemed reasonable to provide a short introduction to the subject.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 1 , Issue 2 , July 1991 , pp. 159 - 178
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

Barr, M. (1979) *-Autonomous categories. Lecture Notes in Mathematics 752. Springer-Verlag, Berlin, Heidelberg, New York.Google Scholar
Chu, P. H(1979) *-Autonomous categories. Lecture Notes in Mathematics 752. Springer-Verlag, Berlin, Heidelberg, New York, Appendix.Google Scholar
Jay, C. B. (1989) Languages for monoidal categories. J. Pure Applied Algebra 59 61–85.CrossRefGoogle Scholar
Eilenberg, S. and Kelly, G. M. (1966) Closed Categories. Proc. Conf. Categorial Algebra (La Jolla, 1965). Springer, pp. 421–562.CrossRefGoogle Scholar
Lafont, Y. (1988) From linear algebra to logic. preprint..Google Scholar
Makkai, M. and Paré, R. Accessible categories. Contemporary Mathematics 104. American Mathematics Society.Google Scholar
Paiva, V.C. V. de (1989a) The Dialecta categories. In: Gray, J. and Scedrov, A. eds, Contemporary Mathematics 92. American Mathematics Society, pp. 47–62.Google Scholar
Paiva, V.C. V. de(1989b)A Dialecta-like model of linear logic. In: Pitt, D. H. et al. , eds Category Theory and Computer Science, Lecture Notes in Computer Science 389 341–356.CrossRefGoogle Scholar
Seely, R. A. G. Linear logic, *-autonomous categories and cofree coalgebrs. In: Gray, J. and Scedrov, A., eds, Categories in computer Science and Logic, Contemporary Mathematics 92. Americal Mathematical Society, pp. 371–382.Google Scholar