Traced Premonoidal Categories

Issue		RAIRO-Theor. Inf. Appl. Volume 37, Number 4, October-December 2003 Fixed Points in Computer Science (FICS'02)


Page(s)		273 - 299
DOI		10.1051/ita:2003020

Theoret. Informatics Appl. 37, 273-299 (2003)
DOI: 10.1051/ita:2003020

Nick Benton¹ and Martin Hyland²

¹ Microsoft Research, Roger Needham Building, 7 J J Thomson Avenue, Cambridge CB3 0FB, UK; nick@microsoft.com.
² University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Wilberforce Road, Cambridge CB3 0WB, UK; M.Hyland@dpmms.cam.ac.uk.

(Received November 12, 2002. Accepted in final form August 14, 2003)

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.

Mathematics Subject Classification. 68N18, 03B70, 03G30

Key words: Traces -- fixed point operators -- premonoidal categories -- recursion -- monads.

© EDP Sciences 2003

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