A Fibrational Framework for Modal Simple Type Theories

Explore a comprehensive tutorial on modal simple type theories within a fibrational framework. Delve into the first part of a series on modal extensions of homotopy type theory, presented by Dan Licata at the Hausdorff Center for Mathematics. Gain insights into the design frameworks and applications of these type theories in synthetic formalizations of topology, differential geometry, and spectra. Discover how this work contributes to real-cohesive and differential-cohesive homotopy type theory. Learn about the connections between modal simple type theories and covering spaces, discrete and codiscrete modalities, and the shape modality in real-cohesive HoTT. Understand the collaborative efforts behind this research, involving contributions from multiple experts in the field.