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Logic and Computation Seminar

Monday, September 27, 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 third talk, I will discuss recent work with Ahrens, Shulman, and Tsementzis in which we build a framework to prove the equivalence principle for higher categorical structures. Our work encompasses bicategories, dagger categories, opetopic categories, and more.