Online Seminar – March 2021 – A/Prof. Emily Riehl

David Wood

  • Thursday
     4 Mar 2021
     9:00 am - 10:00 am

Event Time:
Thursday, 4 March @ 0900 (AEDT) (Melbourne)
Thursday, 4 March @ 0600 (CST) (Beijing, China)
Thursday, 4 March @ 0330 (IST) (New Delhi, India)
Wednesday, 3 March @ 2200 (GMT) (London)
Wednesday, 3 March @ 1700 (EST) (New York)
Wednesday, 3 March @ 1400 (PST) (Seattle)

Presenter: A/Prof. Emily Riehl, Johns Hopkins University

Biography: Johns Hopkins University & Wikipedia

Title: Elements of ∞-Category Theory

Abstract: Confusingly for the uninitiated, experts in infinite-dimensional category theory make use of different definitions of an ∞-category, and theorems in the ∞-categorical literature are often proven “analytically”, in reference to the combinatorial specifications of a particular model. In this talk, we present a new point of view on the foundations of ∞-category theory, which allows us to develop the basic theory of ∞-categories — adjunctions, limits and colimits, co/cartesian fibrations, and pointwise Kan extensions — “synthetically” starting from axioms that describe an ∞-cosmos, the infinite-dimensional category in which ∞-categories live as objects. We demonstrate that the theorems proven in this manner are “model-independent”, i.e., invariant under change of model. Moreover, there is a formal language with the feature that any statement about ∞-categories that is expressible in that language is also invariant under change of model, regardless of whether it is proven through synthetic or analytic techniques. This is joint work with Dominic Verity of Macquarie University.

Structure: 45 minutes seminar with 15 minutes question time

Seminar Recording & Slides:

Please click here for the recording of the webinar

Please click here for the presentation slides