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Feedback, trace and fixed-point semantics
Published online by Cambridge University Press: 15 December 2002
Abstract
We introduce a notion of category with feedback-with-delay, closely related to the notion of traced monoidal category, and show that the Circ construction of [15] is the free category with feedback on a symmetric monoidal category. Combining with the Int construction of Joyal et al. [12] we obtain a description of the free compact closed category on a symmetric monoidal category. We thus obtain a categorical analogue of the classical localization of a ring with respect to a multiplicative subset. In this context we define a notion of fixed-point semantics of a category with feedback which is seen to include a variety of classical semantics in computer science.
- Type
- Research Article
- Information
- RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 2: Fixed Points in Computer Science (FICS'01) , April 2002 , pp. 181 - 194
- Copyright
- © EDP Sciences, 2002
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