The Artin Glueing of F is a presheaf topos. Structures in Comp. The same class of monads also appeared in a recent paper of G.M. Kelly, where they were characterized as the clubs over the free monoid monad in the category of Sets. An important part of concurrency, the study of systems with many activities occurring together, is the study of hybrid dynamical systems.
Hybrid systems are dynamical systems with two levels of description.
On the one hand they are continuous systems whose behaviour is governed by differential equations. The change from one discrete state to another occurs over an interval of time which may be state-dependent, and hence successive discrete actions cannot be identified with regular interval of time. A simple example is a heating system with a temperature controller. Asynchronous circuits provide another class of examples of particular interest in this talk. Several automata models have been proposed for analysing hybrid systems.