Closure properties of coalgebra automata

We generalize some of the central results in automata theory to the abstraction level of coalgebras. In particular, we show that for any standard, weak pullback preserving functor F, the class of recognizable languages of F -coalgebras is closed under taking unions, intersections and projections. Our main technical result concerns a construction which transforms a given alternating F -automaton into an equivalent non-deterministic one.