Abstract algebra seems doable at a young age for a typical child (say, somewhere b/w late middle school and late high school depending on the kid). I've done bi

Abstract algebra seems doable at a young age for a typical child (say, somewhere b/w late middle school and late high school depending on the kid). I've done bits of group theory with kids in that age group before. It usually gets pretty well, but we never get past the first chapter or two. Basic proofs, but it's a good introduction to what "real" math is like. IMO category theory would be a waste of time without first going through a mathematics undergraduate course of study. Getting past the preface of a reasonable book on category theory requires internalizing the idea of a natural transformation. If you can't get that far, you won't get anything non-superficial out of studying category theory. Understanding what a natural transformation is requires at least one example you can relate to. Understanding why it'd be useful to abstract away from that particular example requires knowing enough about at least one other example. And to do anything even moderately interesting in category theory you need a fair bit of mathematical maturity, which means being able to write and read proofs together with a bit of knowledge about modern logic, analysis and algebra. Without that, a lot of the motivation for category theory is kind of lost (and probably most of the available exercise aren't even comprehensible. And learning math without exercises is close to impossible.).