Tags:category theory, distributive law, list monad, monad composition, monads, no-go theorem and powerset monad

Abstract:

While papers showing examples of distributive laws are abundant, papers containing the opposite result - that certain distributive laws cannot exist - are rarely seen. In fact, the only proof technique known to us is in 'Distributing Probability over Nondeterminism' by Varacca and Winskel, which contains a proof by Plotkin that the probability monad does not distribute over the powerset monad. In 2008, Manes and Mulry posed the question of whether the list monad distributes over itself. We solve this question, proving that both the list monad and powerset monad do not distribute over themselves, while there is precisely one distributive law for the multiset monad over itself.

Some No-Go Theorems for Distributive Laws (extended abstract)