Hello, The following preprint is available. Comments are welcome. Title : Whitehead's Theorem in Homotopy Theory of Concurrency Comments : 1) 100 pages, LaTeX2e 2) this is a totally new version, not an update, of the old "Unifying The Globular and The Topological Approach of Dihomotopy" with a lot of new results. Abstract : We introduce the category of flows and an equivalence relation on it called weak dihomotopy. The category of globular CW-complexes introduced in a previous paper can be embedded in a canonical way into the category of flows. This embedding induces a category equivalence from the category of globular CW-complexes up to dihomotopy to the one of flows up to weak dihomotopy. This statement is proved thanks to a directed version of Whitehead's theorem (the one concerning the equivalence between weak homotopy and homotopy for CW-complex). So studying HDA up to dihomotopy is equivalent to working within the category of flows. This setting is better than the one of globular CW-complexes because the category of flows is complete and cocomplete. However it is not cartesian closed. But it does have a closed monoidal structure called tensor product which turns out to correspond to the interleaving of all possible asynchronous executions. In particular, the tensor product of the flow associated to the m-cube by the flow associated to the n-cube is the flow associated to the (m+n)-cube. Url : http://www-irma.u-strasbg.fr/~gaucher/flow.ps http://www-irma.u-strasbg.fr/~gaucher/flow.pdf http://www-irma.u-strasbg.fr/~gaucher/flow.ps.gz http://www-irma.u-strasbg.fr/~gaucher/flow.pdf.gz 23-May-2002 10:28:45 -0300,1864;000000000000-00000000