A model category for the homotopy theory of concurrency

Abstract

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.Comment: 45 pages ; 4 figure ; First paper corresponding to the content of math.AT/0201252 ; final versio