A graphical approach to monad compositions

Techniques for monad compositions can be used to provide a basis for categorical unification in the framework of generalised terms. In [4], we gave results for the many-valued sets of terms, and showed that this composition of set functors can be extended to a monad. In this work we introduce new sufficient conditions for two monads being composable, and show that the construction in [4] also satisfies these new condition. In addition, we give a theorem of structure of the multiplication of the composite monad, i.e. its structure can be determined under certain conditions.