Traced Premonoidal Categories
Microsoft Research, Roger Needham Building, 7 J J Thomson Avenue, Cambridge CB3 0FB, UK; firstname.lastname@example.org.
2 University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Wilberforce Road, Cambridge CB3 0WB, UK; M.Hyland@dpmms.cam.ac.uk.
Accepted: 14 August 2003
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