A theory of enriched sheaves
Cartesian closed categories, quasitopoi and topological universes
Categorical differential geometry
Catégorie homotopique stable d’un site suspendu avec intervalle
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
For any etale topological groupoid (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 .
Closure operators in exact completions.
Compact topologies on locally presentable categories
Continuous fibrations and inverse limits of toposes
Core varieties, extensivity, and rig geometry.
Descent, motives and K-theory.
Extension of the concept of n-function to categories
Le topos étale réel d'un anneau
Local enrichments of categories
Notion of topology for bicategories
Notions of flatness relative to a Grothendieck topology.
On the Grothendieck topologies in the toposes of presheaves
Ordered groupoids and étendues
Quotient systems in Grothendieck topoi
Relative subanalytic sheaves
Given a real analytic manifold Y, denote by the associated subanalytic site. Now consider a product Y = X × S. We construct the endofunctor on the category of sheaves on and study its properties. Roughly speaking, is a sheaf on . 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.
Sheaves and concepts : a model-theoretic interpretation of Grothendieck topoi