Concluding the research we conducted during my visit to the ILLC in Amsterdam, my former supervisor Yde Venema and I proved the complementation lemma for coalgebra automata - a property left open in previous works of Yde and Clemens Kupke. In particular we showed that for every automaton A recognising T-coalgebras (T preserves weak pullbacks and preserves finite sets) there is an automaton A of the same type accepting precisely the pointed coalgebras rejected by A.

We submitted the paper. Once it passed the reviewing process, I will go into the details of it.