Example: the first question on the first problem set [1] shows how the idea of the Least Common Multiple and the Greatest Common Divisor are analogous to ⊤ and ⊥ in PLT, or "any" and "never" in TypeScript. (Specifically, the Join and Meet operations)
LCM and GCD are meet and join (union supertype and intersection subtype in PLT), not top and bottom. Top/any would correspond to the product of all numbers (union of all factors), and bottom/never would correspond to 1 (intersection of all factors).
Oh right, "Lattice" is the word I was looking for. It's been too long. Would that be considered a subset of category theory, a precursor to it, or another field that it somewhat "unifies"?