Lattices do not distribute over powerset

I will show that there is no distributive law of the free lattice
monad over the powerset monad. The proof presented also
works for other classes of lattices such as (bounded)
distributive/modular lattices and also for some variants of the
powerset monad such as the (nonempty) finite powerset monad.
All the definitions and concepts needed will be given in the talk.