# 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

### Schedule

#### Overview

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

Reading:

- Lurie HTT section 1.1

- Kerodon 1.0-1.3
#### Week 3 (10/29/21)

Topic: Constructions in Quasicategories

Speaker: TBD

Reading:

- 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

Reading:

- 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

### Resources

All planned resources are freely posted online.

Higher Topos Theory (Lurie): pdf

An Invitation to Higher Algebra (Mazel-Gee): pdf

Kerodon (Lurie): web

Page Last Updated 02/25/2021