That seems a little silly to me and I think we're splitting hairs with what it means to do category/set theory. I don't know category or set theory, so I hope y

That seems a little silly to me and I think we're splitting hairs with what it means to do category/set theory. I don't know category or set theory, so I hope you will forgive me for using yet another allegory. Let's say I make a type class for Groups (in the abstract algebra sense). The rationale behind this is that there's an algorithm for exponentiation which is O(log(n)) versus the naive O(n) algorithm. So if you make an instance that's a Group, you get to use this fast exponentiation. Sure, to understand and use this type class you have to understand what a Group is. However, I think it's a bit of a stretch to tell someone "in order to use Group you must first learn abstract algebra" because they'll think you're telling them to take a university level course. In actuality, they don't have to know much at all (they don't even need to understand _why_ the exponentiation algorithm works) - they just need to know what is a lawful Group. The first day of the intro to abstract algebra course I took introduced much more information than you'd need to use this made up type class, and I expect the same of the others. Like this is my understanding of Functors/Applicatives/Monads. I kind of know their shape and how to use them. If you asked me about any of the underlying math I would shrug and maybe draw a pig (https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ https://bartoszmilewski.com/2014/10/28/category-theory-for-p...).