21 citations · 60 across the 23 of their papers we have counts for
28 papers · 1 filter
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…
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…
On the dependent product in toposes
Olivia Caramello, Riccardo Zanfa
We give an explicit construction of the dependent product in an elementary topos, and a site-theoretic description for it in the case of a Grothendieck topos.
Denseness conditions, morphisms and equivalences of toposes
Olivia Caramello
We systematically investigate morphisms and equivalences of toposes from multiple points of view. We establish a dual adjunction between morphisms and comorphisms of sites, introdu…
On the geometric theory of local MV-algebras
Olivia Caramello, Anna Carla Russo
We investigate the geometric theory of local MV-algebras and its quotients axiomatizing the local MV-algebras in a given proper variety of MV-algebras. We show that, whilst the the…