Apparaît dans la collection : Toposes Online

We explain the properties of the familiar properties of continuous actions of groups on sets, and then explain how the reasoning involved can be extended to categories of monoid actions. By examining to what extent a topological monoid can be recovered from its topos of actions, we obtain a complete characterization of these toposes in terms of the existence of a point with certain properties. This presentation is based on the recent preprint of the same title.