UCSD Infinity Categories (Math \infty)

Homepage for organizing the infinity category reading group at UCSD.

We will endeavor to understand the theory of infinity categories a la Joyal-Lurie's work. To this end, we will mostly rely on two sources of Lurie, his "Higher Topos Theory" and "Kerodon" both of which are freely available online. Our goal is to avoid getting bogged down in technical details as much as possible, while still absorbing the essence of the material.

Email Max if you have questions or would like to join.

Location: APM 5402
Time: Friday 12pm



Weeks 1-2 will introduce the basic building blocks of modern homotopy theory. The remaining weeks will be dedicated to re-building the standard tools of category theory in the infinity-context. Once we finish with Ch1 of HTT, we will move to HA. The Kerodon parts of the reading are much longer and more detailed. In general, you should be able to get away with reading HTT and supplementing anything you find confusing with the corresponding Kerodon chapter.

Tentative Curriculum

Week 1 (10/15/21)

Topic: Model Category Basics
Speaker: Shangjie
Reading: Pages 68-71 of Mazel-Gee Notes.

Week 2 (10/22/21)

Topic: Quasi-categories, Topological Categories, and Simplicial Categories
Speaker: Max
- Lurie HTT section 1.1
- Kerodon 1.0-1.3

Week 3 (10/29/21)

Topic: Constructions in Quasicategories
Speaker: TBD
- Lurie HTT section 1.2-1.2.7

Week 4 (10/29/21)

Topic: More Constructions
Speaker: TBD
Reading: Lurie HTT section 1.2.8-1.2.11

Week 5 (10/29/21)

Topic: Limits and Colimits
Speaker: TBD
- Lurie HTT section 1.2.12-1.2.14 and 1.2.16 (not 1.2.15)
- Kerodon 7.0-7.3

Further Schedule is TBD


All planned resources are freely posted online.

Higher Topos Theory (Lurie): pdf
An Invitation to Higher Algebra (Mazel-Gee):
Kerodon (Lurie):
Page Last Updated 02/25/2021