nLab pseudo-distributive law


The notion of a pseudo-distributive law is a vertical categorification of that of a distributive law, relating two pseudomonads on a bicategory. There are various different levels of weakness that such a thing can exist at. As with ordinary distributive laws, a pseudo-distributive law governs the lifting of one pseudomonad to the Eilenberg-Moore and Kleisli bicategories of the other.


See any of the references, particularly (Walker), who simplified the definition of Marmolejo (reducing from 8 conditions to 5).



  • Max Kelly, Coherence theorems for lax algebras and for distributive laws, Proceedings of the Sydney Category Seminar 1972-73.
  • Francisco Marmolejo, Distributive laws for pseudomonads, TAC
  • Charles Walker. Distributive laws, pseudodistributive laws and decagons. arXiv:2102.12468 (2021).

Last revised on November 28, 2023 at 10:57:19. See the history of this page for a list of all contributions to it.