A systematic treatment of weak bisimulation and observational congruence on presheaf models is presented. The theory is developed with respect to a "hiding" functor from a category of paths to observable paths. Via a view of processes as bundles , we are able to account for weak morphisms (roughly only required to preserve observable paths) and to derive a saturation monad (on the category of presheaves over the category of paths). Weak morphisms may be encoded as strong ones via the Kleisli construction associated to the saturation monad. A general
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