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Girard quantaloids†

Published online by Cambridge University Press:  04 March 2009

Kimmo I. Rosenthal
Kimmo I. Rosenthal
Affiliation:
Department of Mathematics, Union College, Schenectady, NY 12308, USA
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Abstract

The partially ordered models of linear logic, a logical system developed by J. Y. Girard, turn out to be a class of quantales called Girard quantales. The notion of a quantaloid is a natural categorical generalization of a quantale and is one possible way of keeping track of types. In this paper, Girard quantales are generalized to Girard quantaloids. The general theory is developed and several key examples are studied. Turning our attention to the theory of categories enriched in a bicategory, it is then shown that if G is a Girard quantaloid, then the quantaloids Bim(G), Matr(G), and Mon(G), consisting of G-bimodules, G-matrices and G-monads respectively, are also Girard quantaloids.

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Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 2 , Issue 1 , March 1992 , pp. 93 - 108
Copyright
Copyright © Cambridge University Press 1992

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