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 a

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.