From Coalgebraic to Monoidal Traces

Authors:
Bart Jacobs
Affiliations:
Institute for Computing and Information Sciences, Radboud University of Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2010

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Abstract

The main result of this paper shows how coalgebraic traces, in suitable Kleisli categories, give rise to traced monoidal structure in those Kleisli categories, with finite coproducts as monoidal structure. At the heart of the matter lie partially additive monads inducing partially additive structure in their Kleisli categories. By applying the standard ''Int'' construction one obtains compact closed categories for ''bidirectional monadic computation''.