- 33 pages - version complète de l'article préliminaire de même titre [hal-00194231/fr]International audienceThe primary aim of this work is an intrinsic homotopy theory of strict $\omega$-categories. We establish a model structure on $\omega$-Cat, the category of strict $\omega$-categories. The constructions leading to the model structure in question are expressed entirely within the scope of $\omega$-Cat, building on a set of generation cofibrations and a class of weak equivalences as basic items
Locally partial-ordered spaces (local po-spaces) have been used to model concurrent systems. We provide equivalences for these spaces by constructing a model category containing the category of local po-spaces. We show that the category of simplicial presheaves on local po-spaces can be given Jardine's model structure, in which we identify the weak equivalences between local po-spaces. In the process, we give an equivalence between the category of sheaves on a local po-space and the category ofétale bundles over a local po-space. Finally, we describe a localization that should provide a good framework for studying concurrent systems.
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