  Cattani-Sassone's notion of higher dimensional transition system is
interpreted as a small-orthogonality class of a locally finitely presentable
topological category of weak higher dimensional transition systems. In
particular, the higher dimensional transition system associated with the
labelled n-cube turns out to be the free higher dimensional transition system
generated by one n-dimensional transition. As a first application of this
construction, it is proved that a localization of the category of higher
dimensional transition systems is equivalent to a locally finitely presentable
reflective full subcategory of the category of labelled symmetric precubical
sets. A second application is to Milner's calculus of communicating systems
(CCS): the mapping taking process names in CCS to flows is factorized through
the category of higher dimensional transition systems. The method also applies
to other process algebras and to topological models of concurrency other than
flows.
