Homology, Homotopy and Applications

Volume 5 (2003)

Number 1

A model category for the homotopy theory of concurrency

Pages: 549 – 599

DOI: http://dx.doi.org/10.4310/HHA.2003.v5.n1.a20


Philippe Gaucher (Preuves Programmes et Systèmes, Université Paris 7–Denis Diderot, Paris, France)


We construct a cofibrantly generated model structure on the category of flows such that any flow is fibrant and such that two cofibrant flows are homotopy equivalent for this model structure if and only if they are S-homotopy equivalent. This result provides an interpretation of the notion of S-homotopy equivalence in the framework of model categories.


concurrency, higher dimensional automaton, homotopy, closed monoidal structure, cofibration, compactly generated topological space, cofibrantly generated model category

2010 Mathematics Subject Classification

55Pxx, 68Q85

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