> I think it’s better to at least try to make a name that transmits partial meaning or a general gist of the idea.
If we didn’t use formal terms for math concepts, mathematicians would waste all their time arguing about the colloquial definitions of the colloquial words they tried to map onto abstract concepts. It’s better to have a clean break and force people to learn the specific formal meaning rather than try to limp along on a busted half-intuition.
the terms actually do come from an intuitive place if you look at the underlying math. it's called a functor because it does something function-like - mapping arrows in the domain category to arrows in the codomain. in programming, we think of this as a higher-order function that lifts a function on a category (of types) to a function on a different category (of types). it's only when you try to elide that explanation that the name appears to come from nowhere.
similarly, monads bear a strong resemblance to monoids - in fact, it's the same relationship as functions and functors and it's quite precise. these intuitions only become available to you with the math, though, and programmers have a strange aversion to mathematics for people who do it day in and day out.
If we didn’t use formal terms for math concepts, mathematicians would waste all their time arguing about the colloquial definitions of the colloquial words they tried to map onto abstract concepts. It’s better to have a clean break and force people to learn the specific formal meaning rather than try to limp along on a busted half-intuition.