Course: Synthetic category theory
This course aims to introduce students to the theory of ∞-categories through the recent framework of synthetic category theory developed by Cisinski, Cnossen, Nguyen, and Walde. We will cover the main aspects of ∞-category theory, including:
- Adjunctions
- (Co)cartesian fibrations, left/right fibrations
- (Un)straightening
- Yoneda Lemma
- (Co)limits, left/right Kan extensions
If time permits, we will also explore selected applications of these higher categorical tools.
The course will be taught in parallel by me at Universität Hamburg and by Tashi Walde at Universität Regensburg.
Course schedule
The course will take place during the winter semester 2026/27, which runs from October 12, 2026, to January 30, 2027.
| Week day | Time | Lecture/Exercise | Room |
|---|---|---|---|
| Tuesday | 14-16 | Lecture | MIN-F - Hörsaal 7 |
| Wednesday | 14-16 | Exercise session | MIN-F - Hörsaal 6 |
| Friday | 12-14 | Lecture | MIN-F - Hörsaal 5 |
Lecture notes
Lecture notes are available here.
Exercise sheets are available here: 01, 02, 03, 04, 05.
Zoom information
The course will also be streamed via Zoom. The Zoom information is available on the Moodle page. If you do not have access to it, please send me an email.