21 citations · 60 across the 23 of their papers we have counts for
33 papers
Sites and Grothendieck toposes: an introduction
Olivia Caramello, Laurent Lafforgue
Topos theory occupies a singular place in contemporary mathematics: born from Grothendieck's algebraic geometry, it has emerged as a unifying language for geometry, topology, algeb…
Generation of Grothendieck topologies, provability and operations on subtoposes
Olivia Caramello, Laurent Lafforgue
After reviewing the multiple roles of toposes - as generalized topological spaces, as universal invariants, as categorical analogues of the set-theoretic universe, and as semantic…
On morphisms of relative toposes
Léo Bartoli, Olivia Caramello
We systematically investigate the functors between sites which induce morphisms of relative toposes. In particualar, we establish a relative version of Diaconescu's theorem, charac…
Fibred sites and existential toposes
Olivia Caramello
In the context of relative topos theory via stacks, we introduce the notion of existential fibred site and of existential topos of such a site. These notions allow us to develop re…
Relative topos theory via stacks
Olivia Caramello, Riccardo Zanfa
We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of…
The over-topos at a model
Olivia Caramello, Axel Osmond
With a model of a geometric theory in an arbitrary topos, we associate a site obtained by endowing a category of generalized elements of the model with a Grothendieck topology, whi…