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Issue RAIRO-Theor. Inf. Appl.
Volume 36, Number 2, April-June 2002
Fixed Points in Computer Science (FICS'01)
Page(s) 181 - 194
DOI 10.1051/ita:2002009

Theoret. Informatics Appl. 36, 181-194 (2002)
DOI: 10.1051/ita:2002009

Feedback, trace and fixed-point semantics

P. Katis1, Nicoletta Sabadini1 and Robert F.C. Walters2, 1

1  Dipartimento di Scienze CC. FF.MM.,Università degli Studi dell'Insubria, Como, Italy; nicoletta.sabadini@uninsubria.it.robert.walters@uninsubria.it.
2  School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.


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.


Mathematics Subject Classification. 68Q55, 68Q70, 18D10


© EDP Sciences 2002


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