Using jquery to insert categories into TinyMCE editor

I would like to add a button to the TinyMCE editor that will get the post title and categories and put them into the post (without submitting the post). I can add a button to the editor, but I can’t get the categories. To get the title, I use:

jQuery("#title").val()

This works really well. Is there a way to retrieve the post categories?

I’m fine using JavaScript, but I prefer jQuery. Any suggestions would be appreciated.