Raffaele Lamagna Doctorant Phd advisor : Marc Aiguier et Olivia Caramello

Keywords : Théorie des topos, Topos relatifs, Logique catégorielle

The aim of my thesis is to develop a relative (geometric) logic, i.e. a logic adapted to the description of theories which depend on other theories, as, for example, the theory of modules on a ring depends on the theory of rings. Classical first-order geometric theories can be interpreted naturally in topos. In the same way, a relative geometric theory will have to be interpreted in relative topos.