Algebras for parameterised monads

Authors:
Robert Atkey
Affiliations:
LFCS, School of Informatics, University of Edinburgh, UK
Venue:
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Year:
2009

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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.