coalgebraic-simulation

Checklist

• Introduce HJ-simulation in relator-form, show uniqness of wittnesses.
• Prove a general theorem that symmetric simulation for symmetrized relator yields similarity that is sound and complete for behavioral equivalence (use "Relators and Notions of Simulation Revisited" soundness and compteleness criterion).
• Elaborate this for powerset
• When is symmetrized relator the Barr relator (definition is in "Relators and Notions of Simulation Revisited")?
• At least, try to prove it for the Jacobs-Hughes relator
• Introduce notions of simulation, diverging from HJ-simulation. Do we need two of them (with normalization and without)? How are all of them related?
• Can we separate Hughes-Jacobs relator from one-sided lax relator?