Globular realization and cubical underlying homotopy type of time flow of process algebra
arXiv:0708.3584
Abstract
We construct a small realization as flow of every precubical set (modeling for example a process algebra). The realization is small in the sense that the construction does not make use of any cofibrant replacement functor and of any transfinite construction. In particular, if the precubical set is finite, then the corresponding flow has a finite globular decomposition. Two applications are given. The first one presents a realization functor from precubical sets to globular complexes which is characterized up to a natural S-homotopy. The second one proves that, for such flows, the underlying homotopy type is naturally isomorphic to the homotopy type of the standard cubical complex associated with the precubical set.
arXiv comment31 pages, 1 figure, LaTeX2e
References in corpus (7)
- Combinatorics of branchings in higher dimensional automata
- Homological properties of non-deterministic branchings and mergings in higher dimensional automata
- Homotopical interpretation of globular complex by multipointed d-space
- Comparing globular complex and flow
- T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type
- T-homotopy and refinement of observation (III) : Invariance of the branching and merging homologies
- T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences