The List Monad is defined as a triple $< L , \mu, \eta >$.
$L: Set \rightarrow Set$
$L$ takes a set to the set of all lists on that set.
$\mu : L \cdot L \rightarrow L$
$\mu$ takes a list of lists to a list by just concatenating all the internal lists.
$\eta : I \rightarrow L$
$\eta$ takes every set element and produces the list with just that element.
What, precisely, is the Eilenberg-Moore Category for the List monad? How do we know this? Is it computable from just the data I have given about the List monad?