nLab relative pseudomonad


Categorical algebra

Higher algebra


The notion of relative pseudomonad generalizes that of pseudomonad, to be relative to a 2-functor, analogous to the notion of relative monad in the one-dimensional setting. This enables the construction of Kleisli bicategories of pseudomonads on Prof (e.g. for defining generalized multicategories) by means of pseudo-distributive laws as if the presheaf category construction were a monad with Prof as its Kleisli bicategory, even though it is not for size reasons.

An example is the free cocompletion construction on a small category.


An early observation that the bicategory of profunctors should be a Kleisli category for a relative monad is Appendice I.1(b) of:

Last revised on December 21, 2023 at 20:53:57. See the history of this page for a list of all contributions to it.