Example [efr-0026]

Let F: \mathsf {Set} \to \mathsf {Set} be a functor. Then there is a dynamical systems theory where \mathcal {C} = \mathsf {Set}, \mathcal {A} is constant at \mathsf {Set}, and T(X) = (X,F(X)). It is easy to see that the category of closed dynamical systems in this theory is equivalently the category of F-coalgebras.