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.

Admittedly, a topic in enriched presheaves requires familiarity with at least the foundational notions in enriched category theory. A single two hour seminar will not allow for a gentle introduction, so that I have decided to down-scale the topic.

New Title: Morita Duality and Logics for Coalgebras

If you are disappointed and would like to learn more about the Morita duality for enriched presheaves, feel free to invite me or await the upcoming publication.

On Wednesday, 12 November, I will give a talk in Algebra|Coalgebra seminar at the ILLC in Amsterdam. There I will define the notion of enriched presheaves and define a Morita duality, which I argue to be suitable for the construction of logics for coalgebras in enriched categories.

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From September to November 2008 I am going to visit the ILLC in Amsterdam to work with Yde Venema on coalgebra automata.