Abstract : We discuss the use of relation lifting in the theory of set-based coalgebra. On the one hand we prove that the neighborhood functor does not extend to a relation lifting of which the associated notion of bisimilarity coincides with behavorial equivalence.On the other hand we argue that relation liftings may be of use for many other functors that do not preserve weak pullbacks, such as the monotone neighborhood functor. We prove that for any relation lifting L that is a lax extension extending the coalgebra functor T and preserving diagonal relations, L-bisimilarity captures behavioral equivalence. We also show that if T is finitary, it admits such an extension iff there is a separating set of finitary monotone predicate liftings for T.
https://hal.inria.fr/hal-01539878
Contributeur : Hal Ifip
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Soumis le : jeudi 15 juin 2017 - 15:02:42
Dernière modification le : jeudi 15 juin 2017 - 15:25:48
Document(s) archivé(s) le : mercredi 13 décembre 2017 - 12:29:59
