Abstract Kleisli Structures on 2-categories

TL;DR

This paper extends the theory of Abstract Kleisli structures to 2-categories, allowing for non-strict monad morphisms and 2-cells, and characterizes when a pseudomonad can be reconstructed from such structures.

Contribution

It generalizes Abstract Kleisli structures to 2-categories, incorporating non-strict monad morphisms and 2-cells, and provides conditions for recovering pseudomonads.

Findings

Extended Abstract Kleisli theory to 2-categories.

Incorporated non-strict monad morphisms and 2-cells.

Characterized when pseudomonads can be reconstructed.

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.