- Location and time
Mondays and Tuesdays, 12-13, starting October 9
D1.07 and online
If you would like to attend, please sign up through the Taught Courses Center.- Lecturer
Martin Gallauer
My email is martin.gallauer@warwick.ac.uk- Content
The language of ∞-categories has permeated a large body of modern mathematics, particularly in algebraic geometry and algebraic topology. (Just as the language of ordinary categories has done before that.) This course will teach you the basics of this language. By the end you should be able to read research articles written in the language of ∞-categories, and to tackle more advanced texts developing the theory, such as the books of Lurie, Cisinski or Land.
Here's a
tentativelist of topics Iaim to covercovered:
- simplicial sets, definition of ∞-categories
- first examples and basic language
- constructing ∞-categories
- limits and colimits
- presentability
- stability, spectra,
derived ∞-categoriesoperads, algebras, modulesDespite the long list of topics I want to be rigorous. However, we won't have time to cover many of the proofs (especially the difficult ones).
- Requirements
I will assume familiarity with ordinary category theory. Some algebraic topology would be useful for intuition but it isn't necessary as I will introduce the necessary background material along the way.
- Credit
There are two options to get credit for this course:
I'm open to other possibilities for assessment.
- Doing the exercises in the lecture notes. You don't have to do absolutely every exercise, let alone correctly. But I want to see you followed the course and put some effort into it.
- Writing up a proof for one of the difficult results in the course that I omitted. Before you embark on this please talk to me. I'm happy to make suggestions and give references.
- Lecture notes
Most recent version, complete: 26.12.