A Syntactical Approach to Weak (Bi-)Simulation for Coalgebras

In [19] Rutten introduced the notion of weak bisimulations and weak bisimilarity for coalgebras of the functor F (X) = X +O. In the present paper I will introduce a notion of weak bisimulation for coalgebras based on the syntax of their functors for a large class of functors. I will show that my definition does not only coincide with the definition from [19], but with the definition for labelled transition systems as well. The approach includes a definition of weak bisimulation for Kripke structures, which might be of interest in its own right.