Algebras for Parameterised Monads
Robert Atkey. Algebras for Parameterised Monads
. In Alexander Kurz, Marina Lenisa, and Andrzej Tarlecki, editors, Algebra and Coalgebra in Computer Science, Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009. Proceedings
, volume 5728 of Lecture Notes in Computer Science
, 3-17. Springer, 2009.
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.