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Traced Premonoidal Categories

Published online by Cambridge University Press:  15 January 2004

Nick Benton  and
Martin Hyland
Nick Benton
Affiliation:
Microsoft Research, Roger Needham Building, 7 J J Thomson Avenue, Cambridge CB3 0FB, UK; nick@microsoft.com.
Martin Hyland
Affiliation:
University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Wilberforce Road, Cambridge CB3 0WB, UK; M.Hyland@dpmms.cam.ac.uk.
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Abstract

Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in Cartesian categories.

Keywords

Tracesfixed point operatorspremonoidal categoriesrecursionmonads.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 4: Fixed Points in Computer Science (FICS'02) , October 2003 , pp. 273 - 299
Copyright
© EDP Sciences, 2003

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