This is a PhD course in the autumn term 2024 (study periods 1 and 2).
Note. This course is run as a self-study reading course. Therefore, you must have the motivation and capacity to digest material without teacher presence.
- Teacher (course-responsible): Christian Sattler
We will read Cisinski's book higher categories and homotopical algebra. This book aims to develops the classical model for higher categories, quasicategories, in a more streamlined way than the standard reference by Lurie.
Cisinski's treatment is classical, making key use of excluded middle to show that every simplicial set is cofibrant (cell complex of boundary inclusions). My goal for the reading group is to document the exact modifications needed to develop the model in a constructive setting.
But you can join also if you just want to develop a more solid understanding of the classical model for higher category theory. This is the model Cisinski has in mind for his recent project of developing higher category theory formally (which would be a natural next topic).
Knowledge of category theory is required (see the first chapter of the book to get a feeling for the level).
Every week, we have a meeting to discuss the material you read. We indicate in advance how far to try to read. You give continuous feedback for how far you managed read (and what you have problems with). We then use the meeting to discuss any problems.
Feel free to discuss with each other during the week. People who already know some topics can help others.
For every meeting, someone volunteers in advance to lead and moderate the discussion:
- Go over all the content.
- Make sure everyone is on the same page (not left behind).
- Stop for discussion when requested or needed.
- After the meeting, write a short protocol on Zulip of what we did.
We will maintain a document detailing the modifications needed to develop the theory in a constructive setting.
For PhD students wanting credits, examination is based on:
- active participation,
- leading at least one meeting,
- solving exercises that we may pose along the way,
- an oral discussion exam.
The amount of credits will depend on the length of the reading group and the amount of work you put into it. Let us aim for 7.5 credits. You need to ask your examiner to agree to this (you can tell them the above information about examination).
According to the poll, Monday afternoon is a good meeting time.
The first meeting (mainly organizational) took place on 2024-09-30 at 14–16 in EDIT 8103.
The next two meetings are:
- 2024-10-07 at 15–17 in EDIT ED,
- 2024-10-14 at 15–17 in EDIT ED.
- Denis-Charles Cisinski: Higher Categories and Homotopical Algebra.
We use Zulip for announcements and online discussions.
To create an account, use this link and replace XXX by the acronym of our unit (spam protection).
Our stream is called cisinski-higher-cats.
The stream is organized into topics (Zulip lingo for threads). Feel free to create new topics, for example for questions that you want to discuss. This is useful if you are stuck on something in your weekly reading. Conversely, you can help your fellow students by engaging with and possibly answering their questions.
One benefit of Zulip over Slack and Discord is that it is free software. It also supports LaTeX rendering!
Obtain the approval of your supervisor and examiner. Then contact the course-responsible teacher.