nLab Kleisli 2-category

Idea

The notion of Kleisli 2-category over a 2-monad is the generalization of the notion of Kleisli category over a monad from category theory to 2-category theory (or from 2- to 3-category theory, depending on perspective).

References

Section 2.1.2 of

• Ignacio Lopez Franco, Autonomous Pseudomonoids (pdf)

• Susan Niefield, Exponentiability in homotopy slices of Top and pseudo-slices of Cat (TAC)