Algebras for Parameterised Monads

Publication Information

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, pages 3-17. Springer, 2009.
DOI: 10.1007/978-3-642-03741-2_2

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.