Directed algebraic topology and higher dimensional transition system

Details Directed algebraic topology and higher dimensional transition system Directed algebraic topology and higher dimensional transition system

2009-03-25

arxiv.org/abs/0903.4276v2

New-York Journal of Mathematics 16 (2010), 409-461

Mathematics

Category Theory

42 pages; LaTeX2e

Scientific paper

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.

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