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From the Wikipedia article on monads:
A monad on a category \(C\) consists of an endofunctor \(T: C \rightarrow C\) together with two natural transformations: \(\eta: 1_C \rightarrow T\) (where \(1_C\) denotes the identity functor on \(C\)) and \(\mu: T^2 \rightarrow T\) (where \(T^2\) is the functor \(T \circ T\) from \(C\) to \(C\)). These are required to fulfull the following "coherence" conditions:
\(\mu \circ T\mu = \mu \circ \mu T\) (as natural transformations \(T^3 \rightarrow T\);
\(\mu \circ T\eta = \mu \circ \eta T = 1_T\) (as natural transformations \(T \rightarrow T\); here \(1_T\) denotes the identity transformation from \(T\) to \(T\).
See this section of the wikipedia article on natural transformations for the explanation of the notations \(T \mu\) and \(\mu T\).