Bisimulation and open maps

An abstract deenition of bisimulation is presented. It enables a uniform deenition of bisimulation across a range of diierent models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract deenition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of history-preserving bisimu-lation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tie-up with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has \reenement" operators, though further work is required to justify their appropriateness and understand their relation to previous attempts.