Monad morphism
= Monad morphism
{title2=$\alpha:S\Rightarrow T$}
A <morphism> of <monads> on one <category> is a <natural transformation> $\alpha:S\Rightarrow T$ with $\alpha\eta^S=\eta^T$ and $\alpha\mu^S=\mu^T(T\alpha)(\alpha S)$. These equations preserve the unit and multiplication. A terminal <endofunctor> in a full composition-closed subcategory containing the identity receives a unique such <morphism> from every <monad> whose <functor> belongs to that subcategory.