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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
by marquis-chacha 7y ago
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)
[1]: https://ocw.mit.edu/courses/mathematics/18-s097-applied-category-theory-january-iap-2019/assignments/18-s097iap19ps1.pdf https://ocw.mit.edu/courses/mathematics/18-s097-applied-cate...
- auggierose 7y agoFor that you just need Lattice theory ...
- marquis-chacha 7y agoOh 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"?
- smadge 7y agoLattice theory is it’s own field that exists outside of and before category theory. All lattices form a category, though, but not vice versa.
- deleted 7y ago[deleted]
- hopler 7y agoLCM 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).
- smadge 7y agoI don’t know PLT very well but wouldn’t top/bottom also be considered terminal/initial objects in categorical terms?