YODL on Nostr: It's fascinating. I don't know enough to say what is worth looking up specifically, ...

It's fascinating. I don't know enough to say what is worth looking up specifically, but the progression I saw was simplicity complexes defines as N points in R^N, that are linearly independent, form a N-1 dimensional "pyramid" that has nice properties. You can glue them together into complexes and prove some stuff about them, minor things like unique representation of points "inside" them, with so called barycentric coordinates, etc.
then you can generalize to abstract complexes as just a formal graph of points and show those can be embedded as above. From there you can define "orientation" and a mapping of one dimension to a lower one, and finally a quotient group that captures the properties of "holes and twists" in the complex, the holography groups.
From there I believe you can show you don't need to approximate with "pyramids" at all... and then there's more stuff from there like cohomology that I didn't get to, and more...