# Online: Seminar, Emily Riehl (Johns Hopkins University), Elements of ∞-Category Theory #### calendar\_today Date and Time **February 16, 2021** 10:00AM - 10:00AM EST #### pin\_drop Location **Zoom** ![Emily Rhiel](/sites/g/files/omnuum6611/files/styles/hwp_1_1__960x960_scale/public/mathpicture/files/rhiel.png?itok=G6ndlDOT) **Location:** Zoom **Time:** Tuesday, February 16, 2021, 10:00 AM (Eastern US), 15:00 (UK/Eire), 16:00 (Central Europe), 23:00 (China) **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. **Additional Ways to Join** Join by telephone (use any number to dial in) +1 929 436 2866 +1 312 626 6799 +1 669 900 6833 400 669 9381 China Toll-free International numbers available: [https://harvar](https://harvard.zoom.us/u/aclg6kOggb)[d.zoom.us/u/aclg6kOggb](https://harvard.zoom.us/u/aclg6kOggb) One tap mobile: +19294362866,,779283357# US (New York) Join by SIP conference room system Meeting ID: 779 283 357 <779283357@zoomcrc.com> **Attachments** --- Attachments- [ picture\_as\_pdf Flyer.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/riehl_seminar_feb_16_2021.pdf) --- Share on:- [ Facebook ](#) - [ Twitter ](#) - [ Linkedin ](#) Save: [ Add to calendar calendar\_today ](https://mathpicture.fas.harvard.edu/node/1573860/event-feed.ics) Copy link link