29 October 2020, 14:00, online

Speaker

Ivan Di Liberti, Czech Academy of Sciences

Title

Formal Model Theory and Higher Topology

Abstract

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.

References

Slides of the talk

Ivan Di Liberti's PhD thesis