Theories of Everything with Curt Jaimungal
Theories of Everything with Curt Jaimungal
Theories of Everything
Emily Riehl Makes Infinity Categories Elementary
2 hour 49 minutes Posted Apr 6, 2026 at 6:44 pm.
A Dream for the Future
Exploring Infinity Categories
The Role of Category Theory
Key Concepts of Category Theory
The Curry-Howard Correspondence
Understanding Left Adjoint Functors
The Innate Lemma Explained
Proving the Isomorphism
The Importance of Abstraction
A Crash Course in Category Theory
Introduction to Infinity Category Theory
Fundamental Infinity Groupoids
What Are Infinity Categories?
The Case for Infinity Categories
Transitioning to Homotopy Type Theory
Crash Course in Homotopy Type Theory
Type Constructors Explained
Propositions as Types
Understanding Dependent Types
Identity Types and Their Importance
The Structure of Infinity Groupoids
Hierarchies of Types
The Univalence Axiom
Transitioning to Infinity Category Theory
Simplicial Type Theory Overview
Pre-Infinity Categories Defined
Isomorphisms in Infinity Categories
Computer Formalization in Mathematics
Conclusion and Future Directions
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Show notes
Emily Riehl, one of the world’s leading category theorists, shares her vision for making infinity category theory something undergrads can actually learn. In this talk, she breaks down how rethinking the foundations of math could change the way it’s taught and understood—and why it might redefine what math even is.
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Links:
•⁠ ⁠Emily’s profile: https://emilyriehl.github.io/
•⁠ ⁠Emily’s presentation: https://emilyriehl.github.io/files/undergraduates-TOE.pdf
•⁠ ⁠A Type Theory For Synthetic ∞-Categories (paper): https://arxiv.org/pdf/1705.07442
•⁠ ⁠Could ∞-Category Theory Be Taught To Undergraduates? (paper): https://arxiv.org/pdf/2302.07855
•⁠ ⁠RZK proof assistant: https://rzk-lang.github.io/rzk/en/latest/
•⁠ ⁠Lean Zulip chat: https://leanprover.zulipchat.com/#recentnews
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