We investigate a canonical way of defining bisimilarity of systems when their<br />
semantics is given by a coreflection, typically in a category of transition<br />
systems. We use the fact, from Joyal et al., that coreflections preserve open<br />
morphisms situations in the sense that a coreflection induces a path<br />
subcategory in the category of systems in such a way that open bisimilarity<br />
with respect to the induced path category coincides with usual bisimilarity of<br />
their semantics. We prove that this method is particularly well-suited for<br />
systems with quantitative information: we canonically recover the path category<br />
of probabilistic systems from Cheng et al., and of timed systems from Nielsen<br />
et al., and, finally, we propose a new canonical path category for hybrid<br />
systems.