Types and coalgebraic structure

We relate weak limit preservation properties of coalgebraic type functors F to structure theoretic properties of the class of all F-coalgebras. In particular, we give coalgebraic characterizations for the condition that F weakly preserves pullbacks, kernel pairs or preimages. We also describe regular monos and epis. In case that |F(1)| ≠ 1 we show that F preserves preimages iff for every class of F-coalgebras. The case |F(1)| = 1 is left as an open problem.Dedicated to the memory of Ivan RivalReceived August 29, 2003; accepted in final form July 13, 2004.This revised version was published online in August 2005 with a corrected cover date.