Univalent Foundations and the Equivalence Principle - Benedikt Ahrens
Institute for Advanced Study via YouTube
Overview
Syllabus
Intro
What is a foundation of mathematics?
Outline
Indiscernability of identicals
Violating the equivalence principle
Voevodsky's homotopy lambda calculus
Overview of type theory
Dependent types and functions
Syntax of type theory
Type dependency
Dependent types in pictures
Inference rules and derivations
The singleton type
The type of dependent pairs
The type of dependent functions IL
A dependent function in pictures
The identity type
Some terms that can be defined
Contractible types, propositions and sets
Equivalences
The path type of pairs
Axioms to characterize some path types
Transport along isomorphism
Monoids in type theory
The type of monoids
Monoid isomorphisms
Equivalence principle for set-level structures
EP for categories
Conclusions
Taught by
Institute for Advanced Study