The uniformity principle on traced monoidal categories

Masahito Hasegawa

In Proc. 9th International Conference on Category Theory and Computer Science (CTCS'02), Electronic Notes in Theoretical Computer Science 69 (2003)

Abstract

The uniformity principle for traced monoidal categories has been introduced as a natural generalization of the uniformity principle (Plotkin's principle) for fixpoint operators in domain theory. We show that this notion can be used for constructing new traced monoidal categories from known ones. Some classical examples like the Scott induction principle are shown to be instances of these constructions. We also characterize some specific cases of our constructions as suitable enriched limits.

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Pointers to Related Work

M. Hasegawa, Recursion from cyclic sharing: traced monoidal categories and models of cyclic lambda calculi. In Proc. Typed Lambda Calculi and Applications, Springer LNCS 1210 (1997) pp.196-213.
M. Hasegawa, Models of Sharing Graphs (A Categorical Semantics of Let and Letrec). PhD thesis ECS-LFCS-97-360, University of Edinburgh (1997) / Distinguished Dissertations Series, Springer-Verlag (1999).
A. Joyal, R. Street and D. Verity, Traced monoidal categories. Mathematical Proceedings of the Cambridge Philosophical Society 119(3) (1996) 447-468.
P. Selinger, Categorical structure of asynchrony. In Proc. MFPS 15, ENTCS 20 (1999).

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