Duality for powerset coalgebras

Coalgebras, Stone Duality, Modal Logic

A brief outline of the topics of the course could be as follows. Coalgebras generalise transition systems. Modal logics are the natural logics for coalgebras. Stone duality provides the relationship between coalgebras and modal logic. Furthermore, some basic category theory is needed to understand coalgebras as well as Stone duality. So we will need to learn something about modal logic, about S...

Duality for Some Categories of Coalgebras

Colby]Fuller Duality between Coalgebras

w x In 8 , K. Morita introduced a useful notion of duality between categories of modules, usually called ‘‘Morita duality.’’ He proved that every duality is given by contravariant hom functors defined by a bimodule which is an injective cogenerator for both categories of modules. On the other hand, the equivalences between categories of comodules over a coalgebra w x were characterized by M. Ta...

On descent for coalgebras and type transformations

We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...

Abstract Counterexample-Based Refinement for Powerset Domains

Counterexample-based Refinement for Powerset Domains R. Manevich, J. Field , T. A. Henzinger, G. Ramalingam, and M. Sagiv 1 Tel Aviv University, {rumster,msagiv}@tau.ac.il 2 IBM T.J. Watson Research Center, [email protected] 3 EPFL, [email protected] 4 Microsoft Research India, [email protected] Abstract. Counterexample-guided abstraction refinement (CEGAR) is a powerful technique to scale auto...