Uploaded January 2021 | Updated September 2026, 1 day ago
Dr. Roberta Bonacina (Carl Friedrich von Weizsäcker Center, University of Tübingen): Introduction to Homotopy Type Theory II
Abstract
Homotopy type theory is a vibrant research field in contemporary Mathematics. It aims at providing a foundation of Mathematics extending Martin-Löf type theory with the central notion of univalence, which induces a connection between types and homotopy spaces.
We will begin the short course defining the simple theory of types, and showing how it can be extended to Martin-Löf type theory and then to Homotopy type theory. We will stress the propositions-as-types interpretation between the type theories and intuitionistic logic, and study in detail the notion of equality. Then we will show how classical logic can be done in this intuitionistic setting, allowing to introduce the law of excluded middle and the axiom of choice as axioms. Finally, we will analyse the different definitions of equivalence, which are fundamental to introduce univalence.
Dr. Roberta Bonacina (Carl Friedrich von Weizsäcker Center, University of Tübingen): Introduction to Homotopy Type Theory II
Abstract
Homotopy type theory is a vibrant research field in contemporary Mathematics. It aims at providing a foundation of Mathematics extending Martin-Löf type theory with the central notion of univalence, which induces a connection between types and homotopy spaces.
We will begin the short course defining the simple theory of types, and showing how it can be extended to Martin-Löf type theory and then to Homotopy type theory. We will stress the propositions-as-types interpretation between the type theories and intuitionistic logic, and study in detail the notion of equality. Then we will show how classical logic can be done in this intuitionistic setting, allowing to introduce the law of excluded middle and the axiom of choice as axioms. Finally, we will analyse the different definitions of equivalence, which are fundamental to introduce univalence.
