It's possible to do it using the same D'N'D feature.
You'd have to have the view treated as HTML and have each category live inside
a new UL. You'd then have to specify that each UL is "droppable".
Whether the AJAX call can alert the server which category it was dropped in to
or not I'm not sure. I'd imagine it could.
If I had a bit more spare time I'd do it for you. It can be done though.