## Types and coalgebraic structure

Fachbereich Mathematik und
Informatik

Philipps-Universität
Marburg

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 *Set*_{F} 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.

Tarmo Uustalu