This is a great article. It captures the essence of functors and monads in programming really well without the usual nonsensical analogies from other similar tutorials.

There are just a few tiny pieces missing from the puzzle: the functor and monad laws. They're pretty straight-forward - one would think they're common sense.

For functor, there is the mapping with identity law:

functor.map({ $0 }) == functor

which says that mapping the identity function over a functor results with a value equal to the one we started with

and the law for compositionality

functor.map({ f2(f1($0)) }) == functor.map(f1).map(f2)

which states that mapping a composite function yields the same result as mapping the first function then mapping the second function onto the result of the first map.

For monad, there are 3 additional laws (left identity, right identity and associativity).