Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 22 / 6 / c / i / Solution

If the multiplication in the unit and multiplication of a monad $\mu$ is invertible, the two unit identities of the monadmake both $T\eta$ and $\eta T$ its inverse. Hence idempotence implies equality of the two unit insertions:This is the first implication in the characterization of an idempotent monad.