LMS Hardy Lecture 2025

Emily Riehl (Johns Hopkins University)

Tuesday 24th June 16:00-18:00

Abstract

 

Event: LMS Hardy Lecture in Glasgow 2025

Date & time: 24 June 2025, 4pm-6pm. (The talk itself is 60 minutes+questions, followed by a reception.)

Venue: 311b Seminar Room in the Maths & Stats building (the reception will be in the common room)

Speaker: Emily Riehl (Johns Hopkins University)

Title: From the 1-categorical Yoneda lemma to the ∞-categorical Yoneda lemma

Abstract: A fundamental theorem in category theory, called the Yoneda lemma, states that two objects in a category are isomorphic if and only if the functors they represent are naturally isomorphic. An analogous result holds when ordinary 1-categories are replaced by ∞-categories, but the proof is considerably more complicated. After explaining why this is, we'll show that there is in fact a proof of the ∞-categorical Yoneda lemma that is as simple as the proof of the 1-categorical Yoneda lemma --- provided we change the background foundation system from set theory to homotopy type theory. Time permitting, we'll also explain a "dependent" generalization of the Yoneda lemma that can be thought of as an "arrow induction" principle.

Registration: https://forms.office.com/e/Qw2J8DhfY5

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