It's the concept of categorical commutativity that's what's useful. A collection of types and functions is "commutative" if every way to get from type A to type B yields the same result. It happens a lot in Haskell where most or all of the operations you're interested in commute with each other, which is how Haskell gets its reputation of "if it compiles it works". In particular, if you `fmap` or `bind` two commutative functions, the result becomes commutative, too.