Categories for the Working Mathematician says
Definition. A monad $T= \langle T, \eta, \mu\rangle $ in a category $X$ consists of a functor $T: X \to X$ and two natural transformations
$$\eta : I_X \Rightarrow T, \mu : T^2 \Rightarrow T $$
which make the following diagrams commute
How can the two diagrams in (2) be written as identity equations?