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Logic and Computation Seminar

Monday, September 20, 2021 - 3:30pm

Paige North

University of Pennsylvania


University of Pennsylvania

via Zoom

The Equivalence Principle is an informal principle asserting that equivalent mathematical objects have the same properties.  For example, isomorphic groups should have the same group-theoretic properties, and equivalent categories should have the same category-theoretic properties. Vladimir Voevodsky established Univalent Foundations as a foundation of mathematics (based on dependent type theory) in which this principle cannot be violated -- it is a theorem.


In this second talk, I will discuss how we can prove the equivalence principle for certain structures in Univalent Foundations. I will talk about previous work regarding structures like groups and categories. I will also discuss recent work with Ahrens, Shulman, and Tsementzis regarding structures like higher categories.