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The category of presheaves on a (small) category is a suitable semanticuniverse to study behaviour of various dynamical systems. In particular,presheaves can be used to record the executions of a system and their morphismscorrespond to simulation maps for various kinds of state-based systems. In thispaper, we introduce a notion of bisimulation maps between presheaves (orexecutions) to capture well known behavioural equivalences in an abstract way.We demonstrate the versatility of this framework by working out thecharacterisations for standard bisimulation, $\forall$-fair bisimulation, andbranching bisimulation.

Bisimulation maps in presheaf categories