# Univalence as a New Principle of Logic

Steve Awodey

Carnegie Mellon University

Thursday, October 2, 2014, 3:30 pm

ENA 101

It is often convenient or useful in mathematics to treat isomorphic structures as the same. The Univalence Axiom for the foundations of mathematics elevates this idea to a foundational principle in the setting of Homotopy Type Theory. It states, roughly, that isomorphic structures can be identified. In his talk, Prof. Awodey will explain this principle and how it can be taken as an axiom, and explore the motivations and consequences, both mathematical and philosophical, of making such an assumption.

**Steve Awodey** is an internationally recognized researcher in the areas of category theory and logic, and has also written on the philosophy of mathematics. He received his Ph.D. in mathematics from the University of Chicago in 1997 under the direction of Saunders Mac Lane. In 2012-13, he was a member of the School of Mathematics at the Institute for Advanced Study, where he co-organized a special year devoted to Univalent Foundations of Mathematics along with T. Coquand and V. Voevodsky. Awodey is one of the inventors of Homotopy Type Theory and leads an active research group on that subject at Carnegie Mellon University, where he is a professor of philosophy and mathematics.

*The Mathematics & Philosophy Lectures aim to introduce topics at the intersection of mathematics and philosophy to a general academic audience. They are sponsored by the Departments of Philosophy and Mathematics, PIMS, the Pacific Institute for the Mathematical Sciences, and the Faculty of Science. The events are free & open to the public; a reception follows. *