@johncarlosbaez @pigworker I learned the same thing but the other way round (this is not a coincidence, we were in the same place when it happened). I knew this operation was a monad but didn't know it was the free monad monad
Said in terms of just polynomial functors, the operation p* defined as the least fixpoint of p*(y) = y + p(p*(y)) (that's the least fixpoint of an endofunctor on Poly) is both a monad -* on Poly, and also has the property that p* is a monad on Set for every p