Ivan Di Liberti, Czech Academy of Sciences
Formal Model Theory and Higher Topology
Motivated by the abstract study of semantics, we study the interaction between topoi, accessible categories with directed colimits and ionads. This theory amounts to a categorification of famous construction from general topology: the Scott topology on a poset and the adjunction between locales and topological spaces. This technology is then used in order to establish syntax-semantics dualities. Among the significant contributions, we provide a logical understanding of ionads that encompasses Makkai ultracategories.