Lax Extensions of Coalgebra Functors

  • Johannes Marti
  • Yde Venema
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7399)


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.


coalgebra relation lifting predicate lifting bisimilarity 


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© IFIP International Federation for Information Processing 2012

Authors and Affiliations

  • Johannes Marti
    • 1
  • Yde Venema
    • 1
  1. 1.ILLCUniversity of AmsterdamThe Netherlands

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