On Voevodsky's Univalence Principle - André Joyal

Explore André Joyal's in-depth conference talk on Vladimir Voevodsky's univalence principle, delivered at the Institute for Advanced Study. Delve into key concepts such as anodyne maps, kin complexes, type notation, dependent types, and the theory of Tribe. Examine the relationships between tight theory and Tribe, equivalence, and univariate vibration. Gain insights into Brown vibration categories, universal vibration, and the completion of univariant machines. This comprehensive presentation covers a wide range of topics in mathematical logic and type theory, offering a valuable resource for researchers and advanced students in the field.

Introduction
Joint work
Presentation
Tribe
Clan
Anodyne map
Kin complexes
Retraction
Theory of Tribe
Type notation
Dependent type
Change of parameters
Context extension
Pat objects
Multiple categories
Identity of type A
Brown vibration category
Tight theory vs Tribe
Equivalence
A implies B
Univariate vibration
Small vibration
Universal vibration
Completing univariant machine
Descent