# 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?
- [x] Can we separate Hughes-Jacobs relator from one-sided lax relator?