 

Philippe Gaucher
Directed algebraic topology and higher dimensional transition systems view print


Published: 
November 15, 2010 
Keywords: 
labelled symmetric precubical set, higher dimensional transition system, locally presentable category, topological category, smallorthogonality class, directed homotopy, model category, process algebra 
Subject: 
18C35, 18A40, 18A25, 18F20, 18G55, 68Q85 


Abstract
CattaniSassone's notion of higher dimensional transition system is
interpreted as a smallorthogonality 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 ncube turns out to be the
free higher dimensional transition system generated by one
ndimensional 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.


Author information
Laboratoire PPS (CNRS UMR 7126), Universit{é} Paris 7Denis Diderot, Site Chevaleret, Case 7014, 75205 PARIS Cedex 13, France

