Feedback, trace and fixed-point semantics
Dipartimento di Scienze CC.
FF.MM.,Università degli Studi dell'Insubria, Como, Italy;
2 School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.
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  is the free category with feedback on a symmetric monoidal category. Combining with the Int construction of Joyal et al.  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.
Mathematics Subject Classification: 68Q55 / 68Q70 / 18D10
© EDP Sciences, 2002