PP is not a monad

Monads are mathematical objects that can be understood as "well-structured ways to collect things". Examples include the monad of finite words, the powerset monad P, the multiset monad, etc. In the talk I will explain the definition and provide some intuitions behind it.

Although a composition of two monads is not immediately a monad itself, one often expects typical examples of monads to be composable in some way. As it turns out, however, the composition of the covariant powerset monad P with itself cannot be made a monad. This is unfortunate, since such a monad could be useful for a categorical understanding of alternating automata.

This negative result, joint work with Julian Salamanca, corrects a mistake that has persisted in the literature for a while.