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We construct a small realization as flow of every precubical set (modelingfor example a process algebra). The realization is small in the sense that theconstruction does not make use of any cofibrant replacement functor and of anytransfinite construction. In particular, if the precubical set is finite, thenthe corresponding flow has a finite globular decomposition. Two applicationsare given. The first one presents a realization functor from precubical sets toglobular complexes which is characterized up to a natural S-homotopy. Thesecond one proves that, for such flows, the underlying homotopy type isnaturally isomorphic to the homotopy type of the standard cubical complexassociated with the precubical set.

Globular realization and cubical underlying homotopy type of time flow of process algebra