Summer of Math Exposition

This paper is exactly the same as any other introductory material to category theory. It gives a bunch of definitions and shows how one can manipulate a few things, but I still have no clue why I would want any of that and how is it useful for anything.

This entry lists high-schoolers and undergraduates as part of its target audience. However, I don’t think it is clear for the target audience why they should care about ∞-categories at the end of the introduction. Hence, I’m scoring 2/9 for motivation.

I think the essay is very clear: definitions are understandable; notation is clear; and there are helpful examples here and there. Each chapter builds on each previous one in a clear way. Overall, the essay has a nice structure and is very informative so I’ll score it 7/9 for clarity.

I’ll also score it a 7/9 for novelty and memorability each since this my first introduction to ∞-categories and this essay does a good job of showing how this definition generalises concepts that I already know.

I love category theory as a topic and find it endlessly fascinating so I’m really glad I got to see this. As promised, it was a bit dense to take in all at once but I’ve saved a copy to dig into more thoroughly later. I do think you’ve overshot the target audience a bit though. Just as one example, I can’t see a typical high-school student understanding the sentence, “are also trivially presheaves from the category with one object and one morphism.” Probably not a large number of undergrads either to be honest. It is all really interesting and I do want to learn more about it but I think you’re taking a lot of knowledge for granted that large portions of your audience, sadly, won’t have.

It’s a pretty dense read, especially because of the introduction with a lot of sarcasm.

I would have had an easier time reading this essay if it were condensed down to a couple pages of just the key insight, along with one clear example of how it applies in everyday life.