Algebra and Coalgebra in Computer Science

Volume 5728 of the series Lecture Notes in Computer Science pp 3-17

Algebras for Parameterised Monads

  • Robert AtkeyAffiliated withLFCS, School of Informatics, University of Edinburgh

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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.