It’s a basic, cool, and important fact that spaces and categories have a common generalization in ∞-categories. This is a first step toward realizing an important relationship between space and algebra that opens for modern “homotopy theory” and “higher algebra.” The modern language for big chunks of algebraic topology, geometry, K-theory, … is decidedly ∞-categorical, so I should learn about ∞-categories.

Higher category theory is a big and formal language. I am not sure how to learn it. As a personal project, I decided to keep a journal to track and reflect on my progress. Maybe a serious goal is to read Jacob Lurie’s Higher Topos Theory, but that’s a big book, and not all-encompassing. So I’ll be drawing on many other sources.

I’m texing personal notes for this. The motto is “slow and steady.” I am not trying to prune them, there are mistakes, and my citations are sloppy. (Feel free to point out any mistakes to me.) Maybe they will be useful for something more intentional and comprehensive in the future.

Here are my 2023 notes. Look at how far it’s come!

Here are my 2024 notes. With new and improved tex!