jQuery is not a Monad, a Monad can take any type and it has a join operator that takes a doubly wrapped value and turn it into a singly wrapped one. This means that for it to be a Monad jQuery would have to work on any type, you have to be able to give it a String, Int or DOM and it operates on it consistently. jQuery's .map can only deal with the one type. It does have jquery.map but that would make the Array the Monad (or actually just a Functor) not jQuery.
Many of jQuery's method are specific to DOM manipulation, parsing and the like and not related to Monads in anyway - more like a combinator library like HXT.