Freyd is Kleisli, for arrows

Authors:
Bart Jacobs;Ichiro Hasuo
Affiliations:
Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands;Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands
Venue:
MSFP'06 Proceedings of the 2006 international conference on Mathematically Structured Functional Programming
Year:
2006

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Abstract

Arrows have been introduced in functional programming as generalisations of monads. They also generalise comonads. Fundamental structures associated with (co)monads are Kleisli categories and categories of (Eilenberg-Moore) algebras. Hence it makes sense to ask if there are analogous structures for Arrows. In this short note we shall take first steps in this direction, and identify for instance the Freyd category that is commonly associated with an Arrow as a Kleisli category.