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Timed transition systems are a widely studied model for real-time systems The intention of the paper is twofold: first to show the applicability of the general categorical framework of open maps in order to prove that timed weak bisimulation is indeed an equivalence relation, and, second, to investigate how several categorical (open maps, path-bisimilarity and coalgebra based) approaches to an abstract characterization of bisimulation relate to each other and to timed weak bisimulation, in the setting of timed transition systems.