3 papers
math.CT2025
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…
math.CT2025
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…
math.AG2015
Syntactic categories for Nori motives
Luca Barbieri-Viale, Olivia Caramello, Laurent Lafforgue
We give a new construction, based on categorical logic, of Nori's -linear abelian category of mixed motives associated to a cohomology or homology functor with values in…