Coalgebraic Simulations and Congruences
In a recent article Gorín and Schröder  study \(\lambda \)-simulations of coalgebras and relate them to preservation of positive formulae. Their main results assume that \(\lambda \) is a set of monotonic predicate liftings and their proofs are set-theoretical. We give a different definition of simulation, called strong simulation, which has several advantages:
\(\lambda \) is monotonic
every simulation is strong
every bisimulation is a (strong) simulation
every F-congruence is a (strong) simulation.
if \(\lambda \) is a separating set, then each difunctional strong simulation is an \(F\)-congruence,
if \(\lambda \) is monotonic, then the converse is true: if each difunctional strong simulation is an \(F\)-congruence, then \(\lambda \) is separating.
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