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Catégorie homotopique stable d’un site suspendu avec intervalle

Joël Riou (2007)

Bulletin de la Société Mathématique de France

Cet article présente la construction de la catégorie homotopique stable d’un site suspendu avec intervalle arbitraire. La fonctorialité de cette construction est étudiée, avec des applications à la théorie homotopique des schémas introduite par F. Morel et V. Voevodsky.

Classifying toposes and foliations

Ieke Moerdijk (1991)

Annales de l'institut Fourier

For any etale topological groupoid G (for example, the holonomy groupoid of a foliation), it is shown that its classifying topos is homotopy equivalent to its classifying space. As an application, we prove that the fundamental group of Haefliger for the (leaf space of) a foliation agrees with the one introduced by Van Est. We also give a new proof of Segal’s theorem on Haefliger’s classifying space B Γ q .

Relative subanalytic sheaves

Teresa Monteiro Fernandes, Luca Prelli (2014)

Fundamenta Mathematicae

Given a real analytic manifold Y, denote by Y s a the associated subanalytic site. Now consider a product Y = X × S. We construct the endofunctor S on the category of sheaves on Y s a and study its properties. Roughly speaking, S is a sheaf on X s a × S . As an application, one can now define sheaves of functions on Y which are tempered or Whitney in the relative sense, that is, only with respect to X.

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