  The aim of this paper is to study the points and localising subcategories of
the topos of $M$-sets, for a finite monoid $M$. We show that the points of this
topos can be fully classified using the idempotents of $M$. We introduce a
topology on the iso-classes of these points, which differs from the classical
topology introduced in SGA4. Likewise, the localised subcategories of the topos
$M$-sets correspond to the set of all two-sided idempotent Ideals of $M$.
