Emily Riehl's "Infinity Categories for Undergraduates" Talk on Curt Jaimungal's Podcast

40:00 on the generality of Category Theoretic proofs. My comment:

There seems to me [that] the more abstract proofs don't refer to "accidents" of the particular representations in some field like topology or linear algebra and in that sense they're more fundamental: the reasons the theorems hold are closer to the underlying logic. This is also what Urs Schreiber was saying a week or so ago about Mathematical Physics.

1:09:08 She says she's beyond the stratosphere a lot of the time. See  Emily Riehl Doing Stratospheric Category Theory. See We Do Not Choose Mathematics as Our Profession, It Chooses Us: Interview with Yuri Manin by Mikhail Gelfand.

1:59:44 on equivalences: I think this has metamathematical consequences. These two definitions of equivalence are logically equivalent, but the set-theoretic definitions admit higher non-trivial structure, such as that produced when you use Gödel numbered propositions?


See Another Excellent Talk on HoTT by Steve Awodey and Emily Riehl on Univalent Foundations. And then functions are all functors (2:27:11) and you get this slogan "Naturality is free in ∞-Category theory":


However, she says early on (36:10) in this talk that the connection between the ideas of adjoints in linear algebra and adjunctions (and adjoint functions in a Galois Connection) is merely typographic. See https://ncatlab.org/nlab/show/adjunction and Curt Jaimungal Interview With Urs Schreiber

2:32:08 ∞-Category theory for computers: 



See https://rzk-lang.github.io/rzk/en/latest/.


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Emily Riehl is a really  great movie director too!

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