A bimodule between monads \((S, \eta ', \mu ')\) on \(A\) and \((T, \eta , \mu )\) on \(B\) is a 1-cell \(f:A \to B\) together with a left \(T\)-action \(\alpha \) and a right \(T\)-action \(\beta \) which commute with each other:
A bimodule between monads \((S, \eta ', \mu ')\) on \(A\) and \((T, \eta , \mu )\) on \(B\) is a 1-cell \(f:A \to B\) together with a left \(T\)-action \(\alpha \) and a right \(T\)-action \(\beta \) which commute with each other: