Sign up to save your podcasts
Or
Share Emily Riehl Makes Infinity Categories Elementary
Share to email
Share to Facebook
Share to X
Share to email
Share to Facebook
Share to X
Or
Emily Riehl Makes Infinity Categories Elementary
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.
I subscribe to The Economist for their science and tech coverage. As a TOE listener, get 35% off! No other podcast has this: https://economist.com/TOE
Join My New Substack (Personal Writings): https://curtjaimungal.substack.com
Listen on Spotify: https://tinyurl.com/SpotifyTOE
Become a YouTube Member (Early Access Videos):
https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join
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
Timestamps:
00:00 A Dream for the Future
01:55 Exploring Infinity Categories
03:54 The Role of Category Theory
10:17 Key Concepts of Category Theory
12:01 The Curry-Howard Correspondence
15:37 Understanding Left Adjoint Functors
24:38 The Innate Lemma Explained
38:29 Proving the Isomorphism
41:50 The Importance of Abstraction
44:04 A Crash Course in Category Theory
44:17 Introduction to Infinity Category Theory
56:27 Fundamental Infinity Groupoids
1:03:34 What Are Infinity Categories?
1:09:12 The Case for Infinity Categories
1:18:12 Transitioning to Homotopy Type Theory
1:22:49 Crash Course in Homotopy Type Theory
1:30:56 Type Constructors Explained
1:34:19 Propositions as Types
1:42:50 Understanding Dependent Types
1:49:01 Identity Types and Their Importance
1:54:03 The Structure of Infinity Groupoids
1:59:33 Hierarchies of Types
2:06:19 The Univalence Axiom
2:08:36 Transitioning to Infinity Category Theory
2:10:04 Simplicial Type Theory Overview
2:14:56 Pre-Infinity Categories Defined
2:24:32 Isomorphisms in Infinity Categories
2:31:48 Computer Formalization in Mathematics
2:40:02 Conclusion and Future Directions
Support TOE on Patreon: https://patreon.com/curtjaimungal
Twitter: https://twitter.com/TOEwithCurt
Discord Invite: https://discord.com/invite/kBcnfNVwqs
#science
Learn more about your ad choices. Visit megaphone.fm/adchoices
View all episodes
By Theories of Everything
5
1313 ratings
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.
I subscribe to The Economist for their science and tech coverage. As a TOE listener, get 35% off! No other podcast has this: https://economist.com/TOE
Join My New Substack (Personal Writings): https://curtjaimungal.substack.com
Listen on Spotify: https://tinyurl.com/SpotifyTOE
Become a YouTube Member (Early Access Videos):
https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join
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
Timestamps:
00:00 A Dream for the Future
01:55 Exploring Infinity Categories
03:54 The Role of Category Theory
10:17 Key Concepts of Category Theory
12:01 The Curry-Howard Correspondence
15:37 Understanding Left Adjoint Functors
24:38 The Innate Lemma Explained
38:29 Proving the Isomorphism
41:50 The Importance of Abstraction
44:04 A Crash Course in Category Theory
44:17 Introduction to Infinity Category Theory
56:27 Fundamental Infinity Groupoids
1:03:34 What Are Infinity Categories?
1:09:12 The Case for Infinity Categories
1:18:12 Transitioning to Homotopy Type Theory
1:22:49 Crash Course in Homotopy Type Theory
1:30:56 Type Constructors Explained
1:34:19 Propositions as Types
1:42:50 Understanding Dependent Types
1:49:01 Identity Types and Their Importance
1:54:03 The Structure of Infinity Groupoids
1:59:33 Hierarchies of Types
2:06:19 The Univalence Axiom
2:08:36 Transitioning to Infinity Category Theory
2:10:04 Simplicial Type Theory Overview
2:14:56 Pre-Infinity Categories Defined
2:24:32 Isomorphisms in Infinity Categories
2:31:48 Computer Formalization in Mathematics
2:40:02 Conclusion and Future Directions
Support TOE on Patreon: https://patreon.com/curtjaimungal
Twitter: https://twitter.com/TOEwithCurt
Discord Invite: https://discord.com/invite/kBcnfNVwqs
#science
Learn more about your ad choices. Visit megaphone.fm/adchoices
More shows like Theories of Everything with Curt Jaimungal
View all
Philosophize This!
15,229 Listeners
Making Sense with Sam Harris
26,380 Listeners
EconTalk
4,270 Listeners
Philosophy For Our Times
316 Listeners
Into the Impossible With Brian Keating
1,065 Listeners
The Michael Shermer Show
941 Listeners
TRIGGERnometry
2,275 Listeners
Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
4,167 Listeners
Danny Jones Podcast
1,272 Listeners
Fall of Civilizations Podcast
5,239 Listeners
Within Reason
1,662 Listeners
Theories of Everything with Curt Jaimungal
18 Listeners
Honestly with Bari Weiss
8,447 Listeners
American Alchemy with Jesse Michels
428 Listeners
The Last Invention
1,149 Listeners