Left Exact Modalities in Type Theory

I will discuss a recognition principle for left exact modalities in homotopy type theory and explain how it relates to the problem of understanding subtopoi of $\infty$-topoi. This theory generalizes the classical theory of Lawvere-Tieney topologies to the case of higher topoi. I will also describe some new phenomena which arise in the higher dimensional case.

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.