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Algebras for parameterised monads

Atkey, Robert (2009) Algebras for parameterised monads. In: Algebra and Coalgebra in Computer Science, Third International Conference, CALCO 2009. Lecture Notes in Computer Science, 5728 . Springer, pp. 3-17.

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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.