  We generalize the work by Soboci\'nski on relational presheaves and their
connection with weak (bi)simulation for labelled transistion systems to a
coalgebraic setting. We show that the coalgebraic notion of saturation studied
in our previous work can be expressed in the language of lax functors in terms
of existence of a certain adjunction between categories of lax functors. This
observation allows us to generalize the notion of the coalgebraic weak
bisimulation to lax functors. We instantiate this definition on two examples of
timed systems and show that it coincides with their time-abstract behavioural
equivalence.
