%0 Conference Proceedings
%T Lax Extensions of Coalgebra Functors
%+ Institute for Logic, Language and Computation (ILLC)
%A Marti, Johannes
%A Venema, Yde
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 11th International Workshop on Coalgebraic Methods in Computer Science (CMCS)
%C Tallinn, Estonia
%Y Dirk Pattinson
%Y Lutz Schröder
%I Springer
%3 Coalgebraic Methods in Computer Science
%V LNCS-7399
%P 150-169
%8 2012-03-31
%D 2012
%R 10.1007/978-3-642-32784-1_9
%K coalgebra
%K relation lifting
%K predicate lifting
%K bisimilarity
%Z Computer Science [cs]Conference papers
%X 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.
%G English
%2 https://inria.hal.science/hal-01539878/document
%2 https://inria.hal.science/hal-01539878/file/978-3-642-32784-1_9_Chapter.pdf
%L hal-01539878
%U https://inria.hal.science/hal-01539878
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-CMCS
%~ IFIP-LNCS-7399
%~ IFIP-ETAPS