Great comment, thank you. Also, bravely asking these obvious, "stupid", elephant-in-the-room, naive questions on HN is a great place for a discussion to start, and will attract people who can explain things in simple terms. The comments will be more useful reading to more people than ones on a high, technical level. 'Being wrong on the internet' attracts truth. It's not the experts who will object to such questions!
And as a complete non-expert in this subfield of math (or anything within a hundred miles of it) I would love to hear why people are saying stuff like "equality is a fundamental mistake of mathematics and this approach is fixing it" rather than "this approach is developing a more refined/general/flexible notion of equality".
After a few minutes of deferential throat clearing, I'd like to say "in all seriousness, come on, equality isn't a mistake, and whatever brilliant insight your theory affords still isn't going to do away with it."