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.