- Lax Extensions of Coalgebra Functors
- Coalgebraic methods in computer science: 11th international workshop, CMCS 2012
- Book/source title
- Coalgebraic Methods in Computer Science
- Book/source subtitle
- 11th International Workshop, CMCS 2012, colocated with ETAPS 2012, Tallinn, Estonia, March 31 – April 1, 2012 : revised selected papers
- Pages (from-to)
- Heidelberg: Springer
- ISBN (electronic)
- Lecture Notes in Computer Science: 0302-9743
- Volume (Serie)
- Document type
- Conference contribution
- Interfacultary Research Institutes
Faculty of Science (FNWI)
- Institute for Logic, Language and Computation (ILLC)
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.
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