Solution
= Solution
With $T=GF$, unit $\eta$ and multiplication $G\varepsilon F$, the <Eilenberg-Moore comparison functor> is
$$
\boxed{K:\mathcal D\to\mathcal C^T,\qquad Kd=(Gd,G\varepsilon_d),\qquad K(h)=Gh.}
$$
Here $G\varepsilon_d:T(Gd)=GFGd\to Gd$ is the <monad algebra> action, and the underlying <functor> satisfies $UK=G$. The triangle identities and counit <naturality> provide the <monad algebra> laws and the compatibility of $Gh$, as required for this definition.