> You are effectively saying you cant define anything unless you include every case, which is clearly nonsense.
No I'm not. I will repeat what I said again: such things are defined by their general mathematical definition, and any analogy can only speak for certain subsets of examples of that definition.
> The transform is "transform the wrapped properties into some IO call", and all transforms are explicitly sequential.
How exactly does the mathematical definition of a monad say anything about "transforms"?
The word "transformation" in that name has absolutely nothing to do with your use of the word "transform" ("transform the wrapped properties into some IO call"). MacLane could have decide to call natural transformations "widgets". My point is, besides the name (which is completely arbitrary), why would you even begin to believe this has something to do with "transforming properties into IO calls"?
The transformation mentioned there has nothing to do with using the bind operator within a monad. An example of a natural transformation would be transforming from one monad to another monad
No I'm not. I will repeat what I said again: such things are defined by their general mathematical definition, and any analogy can only speak for certain subsets of examples of that definition.
> The transform is "transform the wrapped properties into some IO call", and all transforms are explicitly sequential.
How exactly does the mathematical definition of a monad say anything about "transforms"?
I think you didn't actually read my comment.