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.
@article{ITA_2002__36_2_181_0,
author = {Katis, P. and Sabadini, Nicoletta and Walters, Robert F. C.},
title = {Feedback, trace and fixed-point semantics},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {36},
year = {2002},
pages = {181-194},
doi = {10.1051/ita:2002009},
mrnumber = {1948768},
zbl = {1050.68100},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2002__36_2_181_0}
}
Katis, P.; Sabadini, Nicoletta; Walters, Robert F. C. Feedback, trace and fixed-point semantics. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) pp. 181-194. doi : 10.1051/ita:2002009. http://gdmltest.u-ga.fr/item/ITA_2002__36_2_181_0/
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