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      Freyd is Kleisli, for Arrows

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      Workshop on Mathematically Structured Functional Programming (MSFP 2006) (MSFP)

      Mathematically Structured Functional Programming

      2 July 2006

      Arrow, Freyd Category, Kleisli Category, Algebra

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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.

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          Most cited references 8

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          The formal theory of monads

           Ross Street (1972)
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            Generalising monads to arrows

             John Hughes (2000)
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              Premonoidal categories and notions of computation

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                Author and article information

                Contributors
                Conference
                July 2006
                July 2006
                : 1-13
                Affiliations
                Institute for Computing and Information Sciences, Radboud University Nijmegen

                Postbus 9010, 6500 GL Nijmegen, The Netherlands
                Article
                10.14236/ewic/MSFP2006.9
                © Bart Jacobs et al. Published by BCS Learning and Development Ltd. Workshop on Mathematically Structured Functional Programming (MSFP 2006), Kuressaare, Estonia

                This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

                Workshop on Mathematically Structured Functional Programming (MSFP 2006)
                MSFP
                Kuressaare, Estonia
                2 July 2006
                Electronic Workshops in Computing (eWiC)
                Mathematically Structured Functional Programming
                Product
                Product Information: 1477-9358BCS Learning & Development
                Self URI (journal page): https://ewic.bcs.org/
                Categories
                Electronic Workshops in Computing

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