Abstract Kleisli structures on $2$-categories
Published in Electronic Proceedings in Theoretical Computer Science 429 (2025), 29–48, 2025
Recommended citation: Miranda, A. (2025). Abstract Kleisli Structures on 2-categories. Electronic Proceedings in Theoretical Computer Science 429, 29–48. https://doi.org/10.4204/EPTCS.429.2 https://doi.org/10.4204/EPTCS.429.2
Abstract
Fuhrmann introduced Abstract Kleisli structures to model call-by-value programming languages with side effects, and showed that they correspond to monads satisfying a certain equalising condition on the unit. We first extend this theory to non-strict morphisms of monads, and to incorporate $2$-cells of monads. We then further extend this to a theory of abstract Kleisli structures on $2$-categories, characterising when the original pseudomonad can be recovered by the abstract Kleisli structure on its $2$-category of free-pseudoalgebras.