  We define a notion of Lambda-simulation for coalgebraic modal logics,
parametric on the choice Lambda of predicate liftings for a functor T. We show
this notion is adequate in several ways: i) it preserves truth of positive
formulas, ii) for Lambda a separating set of monotone predicate liftings, the
associated notion of Lambda-bisimulation corresponds to T-behavioural
equivalence (moreover Lambda-n-bisimulations correspond to T-n-behavioural
equivalence), and iii) in fact, for Lambda-separating and T preserving weak
pullbacks, difunctional Lambda-bisimulations are T-bisimulations. In essence,
we arrive at a modular notion of equivalence that, when used with a separating
set of monotone predicate liftings, coincides with T-behavioural equivalence
regardless of whether T preserves weak pullbacks (unlike the notion of
T-bisimilarity).
