Institute of Information Science, Academia Sinica

State-based systems can often be modelled as coalgebras in terms of category theory such as streams, finite and infinite trees, (non)deterministic state machines, Kripke frames/models, Markov chains, Markov processes, Segala systems, alternating systems, to name but a few. Recently, this notion has been used in unifying different notions and results, e.g., Eilenberg's theorem on varieties of languages and Brzozowski's minimization algorithm. In this talk, I will give a glimpse of coalgebras in theoretical computer science with a crash course of basic category theory.