nLab weak distributive law

Weak distributive laws


Higher algebra

2-Category theory

Weak distributive laws


The notion of a weak distributive law between two monads is a generalisation of that of a distributive law, in which forming the composite monad requires splitting an idempotent on the underlying composite endofunctor.


See also weak bimonad.

Weak distributive laws among monads:

For the weak mixed distributive law (monad and comonad) version see

2-categorical context in the sense of formal theory of monads is also exposed in

An application of weak distributive laws to explain Street’s weak wreath products (comparable to the treatment of wreaths in bicategories) and also related bilinear factorization structures

Last revised on April 26, 2023 at 11:49:04. See the history of this page for a list of all contributions to it.