I am very much interested in finding out about any category theoretical work on dynamical systems and on ergodic theory. On the face of it, it seems that a categorical language can go a long way, at least this is my impression by reading the first few pages of the great book by Furstenberg, ``Recurrence in Ergodic Theory and Combinatorial Number Theory.'' I have also seen some categorical language used in Terry Tao's lectures on ergodic theory (MATH 254A : Topics in Ergodic Theory.) Does anyone know of any other work? Especially, are there non-trivial results in ergodic theory that are proven using categorical constructions and theorems?