List monad
= List monad
{title2=$\mathrm{List}(X)=\coprod_{n\geq0}X^n$}
= Free monoid monad
{synonym}
On the <Category of sets>, the list <monad> sends $X$ to all finite ordered lists of elements of $X$, including the empty list. Its unit inserts a singleton list and its multiplication concatenates a list of lists. Functoriality is entrywise application of functions. Ordered flattening proves the monad laws. This is the free-<monoid> monad, so order must not be discarded.