Open maps and observational equivalences for timed partial order models

The intention of the paper is to show the applicability of the general categorical framework of open maps to the setting of timed extensions of partial order models, in order to transfer general concepts of equivalences to the models. In particular, we define categories of timed event structures, whose morphisms are to be thought of as simulations, and accompanying (sub)categories of observations, to which the corresponding notions of open maps are developed. We then use the open maps framework to obtain abstract bisimilarities which are established to coincide with timed extensions of well-known partial order based equivalences.