We discuss the use of relation lifting in the theory of set-based coalgebra and coalgebraic logic. 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 behavioral equivalence. On the other hand we argue that relation liftings may be of use for many other functors that do not preserve weak pullb...

We prove that if (X,A, P ) is an arbitrary probability space with countably generated σ-algebra A, (Y,B,Q) is an arbitrary complete probability space with a lifting ρ and R̂ is a complete probability measure on A ⊗̂R B determined by a regular conditional probability {Sy :y ∈ Y } on A with respect to B, then there exist a lifting π on (X × Y,A ⊗̂R B, R̂) and liftings σy on (X, Ây, Ŝy), y ∈ Y , such ...

We study liftings of holomorphic maps into some Teichmüller spaces. We also study the relationship between universal holomorphic motions and holomorphic lifts into Teichmüller spaces of closed sets in the Riemann sphere.