The theory of Universal Coalgebra, pioneered by Jan Rutten (CWI), offers a unified framework for studying diverse types of state based systems, useful in stream programming, object oriented programming, automata theory, Kripke Structures, probabilistic transition systems, and even topological spaces. The type of a coalgebra is determined by the choice of a Set functor F and the functorial properties of F, such as accessibility, separability, or preservation of certain types of limits, determine the structural and logical properties of the associated class of coalgebras.

In this talk we give a survey of the interplay of functorial conditions and associated structural properties.