Profunctors, open maps and bisimulation

@article{Cattani2005ProfunctorsOM,
  title={Profunctors, open maps and bisimulation},
  author={Gian Luca Cattani and Glynn Winskel},
  journal={Mathematical Structures in Computer Science},
  year={2005},
  volume={15},
  pages={553 - 614}
}
This paper studies fundamental connections between profunctors (that is, distributors, or bimodules), open maps and bisimulation. In particular, it proves that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation. Consequently, the composition of profunctors preserves open maps as 2-cells. A guiding idea is the view that profunctors, and colimit preserving functors, are linear maps in a model of classical linear… 
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