Tuesday, 12 March 2002, 11:00
Cybernetica Bldg (Akadeemia tee 21), room B216
Abstract: Properties of the type functor F influence strongly the structure theory of the class SetF of all F-coalgebras. In the early days of universal coalgebra, authors assumed F to preserve weak pullbacks. Subsequently, it has turned out that the core theory can be developed without this assumption.
Still, preservation properties of F entail additional structure theoretical consequences. If, for instance, F preserves weak pullbacks, then the largest bisimulation on any coalgebras is transitive, indistinguishability is the same as observational equivalence, congruences are bisimulations and monos are injective.
We separately consider the cases where F weakly preserves pullbacks, preimages, kernels, and coequalizers. In each case we find structural properties for the class of all F-coalgebras that are determined by such preservation assumptions.