The point is not to be snug about it. Functional programming (and monads) are actually simpler. You just need to resist the urge to "make it more understandable".
Abstract math doesn't have good analogies to the real world. By trying to make an analogy with the concrete ("monads are mappable") you lose simplicity.
They are supposed to help you build better foundations; the abstractions to better understand your complexity you need to build (or at least pick) yourself.
Good foundations then help you relate the abstractions. For example, the categoric dual of a product is a sum. We can apply it to relation (relational algebra), and we get that sum is data inheritance.
So that gives you understanding of how functions (foreign keys), product (relation) and sum (inheritance) fit together. This sometimes helps to build abstractions in a consistent way.