Algebraic Topology 616:
the model-independent theory of ∞-categories
A draft version of the syllabus can be found here.
The primary course text was a textbook-in-progress, co-written with Dominic Verity, that was drafted as we progressed:
For a preview of the material that we will discuss over the course of the semester, see:
- ∞-category theory from scratch lecture notes written to accompany a four-hour mini course on these topics. Videos of these lectures can be found here.
- A half hour talk outlining a program to develop the foundations of (∞,2)-category theory by sketching the historical development leading to the model-independent theory of (∞,1)-categories that will be the focus of this course.
Background category theory can be found in Category Theory in Context or any text that the reader prefers. Background on simplicial sets can be gathered by osmosis or from any introductory text of the reader's choosing.
For guided self-study of some topics in category theory and in the theory of simplicial sets that will be relevant for us, I recommend working through the following exercises before the term begins:
Question and answer sessions are open to everyone (whether or not you've solved any exercises) and any topic is open for discussion. What follows are a list of suggested exercises that may guide our discussion.
- Monday, February 5: Exercises 1-2 from the prerequisite problem set; 1.1.i-iv, 1.1.vi, 1.2.i.
- Monday, February 19: 2.1.i, 2.2.ii, 2.3.i, 2.3.ii, 2.4.i, 2.4.ii
- Monday, March 12: your choice of 3.3.i or 3.3.ii, 4.2.i, 4.3.i, 4.4.i, 5.1.iv
If you have any questions about the course, please get in touch. My contact info can be found on my personal website.