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Algebras for Parameterised Monads

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Book cover Algebra and Coalgebra in Computer Science (CALCO 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5728))

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Abstract

Parameterised monads have the same relationship to adjunctions with parameters as monads do to adjunctions. In this paper, we investigate algebras for parameterised monads. We identify the Eilenberg-Moore category of algebras for parameterised monads and prove a generalisation of Beck’s theorem characterising this category. We demonstrate an application of this theory to the semantics of type and effect systems.

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Author information

Authors and Affiliations

  1. LFCS, School of Informatics, University of Edinburgh, UK

    Robert Atkey

Authors
  1. Robert Atkey
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Alexander Kurz

  2. Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze, 206, 33100, Udine, Italy

    Marina Lenisa

  3. Faculty of Mathematics, Informatics and Mechanics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Andrzej Tarlecki

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© 2009 Springer-Verlag Berlin Heidelberg

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Atkey, R. (2009). Algebras for Parameterised Monads. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds) Algebra and Coalgebra in Computer Science. CALCO 2009. Lecture Notes in Computer Science, vol 5728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03741-2_2

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  • DOI: https://doi.org/10.1007/978-3-642-03741-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03740-5

  • Online ISBN: 978-3-642-03741-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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