It's pretty close to how both Moggi and Wadler formulated it in their respective seminal papers which introduced monads for representing different notions of computations in functional languages.
Well of course, but arguably there's not much space between "monads-as-containers/burritos" and "monoids-in-the-category-of-endofunctors" presentations...
If you know a better one in between I'm all ears :)