For a specific coalgebra one often uses an (ad hoc) transition notation `x -> y', possibly with labels. This talk will discuss a uniform way to associate such a transition relation with a coalgebra, of a polynomial functor F over Sets. More precisely, it will introduce a canonical functor
CoAlg(F) --> CoAlg(P)
from the category of F-coalgebras to the category of powerset coalgebras (or unlabeled transition systems). This functor will be defined via the temporal logic for coalgebras.
In the end, it will also be shown how a labeled transition system can be obtained, from such an F-coalgebra.