I'm a huge fan of Haskell and the language uses many concepts from category theory, such as monads, functors, and applicatives. However, these are all abstractions which are simple enough to not need any basis in mathematics. I tried to read resources on category theory to understand its motivation, but unlike real math where theorems actually seem to contain new insight, I never found such a thing in category theory.
The entire body of CT has just a small handful of what anyone would consider theorems or lemmas. It’s mostly just stacked definitions.
This is a set. This is a mapping. This is a set of sets. This is a mapping from elements to elements. This is a mapping from elements to sets. This is a mapping from sets to sets. This is the inverse mapping…. Chapter after chapter.
But then there’s “insight” that all of mathematics can be cast as CT, because… all math is just things that map to things! Whoa, far out, dude. Mind is blown.
