Very well said. The practical reality is that the “category theory” used in functional programming paradigms (like Haskell’s) has only a passing resemblence to formal category theory in mathematics. It’s a nice idea to formalize some concepts in functional programming algebraically, but learning formal category theory won’t realistically improve your programming ability. There is some conceptual overlap, but they’re just very different things.
On the one hand I know what you mean: I know practically no category theory (basically I know enough to expect "co" as a prefix to mean "everything the other way around"), but I can still produce good Haskell code.
But on the other hand, I look at some of the stuff Edward Kmett has produced, particularly his lens library which I use all the time, and its very obvious that the design has been informed by a deep knowledge of category theory.
