Open Maps and Trace Semantics 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 partial order models with a dense time domain. In particular, we define a category of timed event structures, where the morphisms are to be thought of as simulations, and an accompanying (sub)category of timed pomsets which provides us with a notion of open maps. Then, we show that the abstract equivalence obtained from the framework of open maps coincides with a timed extension of the well-known trace equivalence based on Pratt’s partial orders.