5
$\begingroup$

To have the composition of two monads be a monad itself, we need a distributive law natural transformation satisfying certain coherence laws.

I'm interested in the strict 2-monad case, i.e. a strict 2-functor equipped with unit and counit natural transformations that satisfy the zig-zag equations on the nose.

I presume in such a case it's still possible for the distributive law to satisfy its coherence laws only up to a modification. If so, what coherence laws do those modifications have to satisfy?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

These are known as pseudo-distributive laws and are the most common notion of distributive law of 2-dimensional monads, even when both 2-dimensional monads in question are strict (i.e. 2-monads rather than pseudomonads). These have been well studied, and there are many equivalent formulations of the coherence conditions. The most comprehensive account is Walker's Distributive laws, pseudodistributive laws and decagons.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .