# nLab pseudo-distributive law

Pseudo-distributive laws

### Context

#### Categorical algebra

internalization and categorical algebra

universal algebra

categorical semantics

#### 2-Category theory

2-category theory

Definitions

Transfors between 2-categories

Morphisms in 2-categories

Structures in 2-categories

Limits in 2-categories

Structures on 2-categories

# Pseudo-distributive laws

## Idea

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.

## Definition

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

## References

• 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 preprint arXiv:2102.12468 (2021).

Last revised on December 16, 2022 at 17:14:03. See the history of this page for a list of all contributions to it.