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Abstract: This article is about the foundation of the Mayer–Vietoris exact sequence in Čech cohomology, with respect to the augmented Čech complex, often called “the stable Koszul complex”. Our treatment is elementary and uses neither the local cohomology of Grothendieck nor the widespread noetherian local cohomology. We use explicit objects giving us an elementary algebraic treatment in a general nonnoetherian context, i.e. two finite sequences , of a commutative ring and some Čech complexes built from these sequences. More precisely, our strategy consists in producing a short exact sequence of “type Čech“ complexes having the expected cohomologies. Then arises a simplicial complex on the set with a relatively surprising combinatory. [Copyright &y& Elsevier]

Globular CW-complexes and flows are both geometric models of concurrent processes which allow to model in a precise way the notion of dihomotopy. Dihomotopy is an equivalence relation which preserves computer-scientific properties like the presence or not of deadlock. One constructs an embedding from globular CW-complexes to flows and one proves that two globular CW-complexes are dihomotopic if and only if the corresponding flows are dihomotopic. To cite this article: P. Gaucher, C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright &y& Elsevier]