The spongey mess below on the left is \(M^2(d)\). Because this
monstrosity is structured monadically, \(\mu :: M^2 \to M\)
provides a clean way to identify each state in the dynamical
system with states in \(M(d)\).
Computing \(\mu :: M^2 \to M\) associates every state on the
left to some state on the right. Here, this is indicated by
color matching. The fixed points go to fixed points and
(surprisingly) every other state folds onto a state
which preserves dynamics.