AJAX: Visitor Selects Category. How to Get Widgets Updated w/Selected Cat

Good Evening,

I am interested in finding out if by having a site visitor select from a drop-down list of categories, widgets with posts tagged by that category can be populated.

Is this possible through AJAX? I’m having a bit of a hard time understanding how to make the connection between the category selection and getting the Widgets set up so that it displays the posts tagged by that selected Category.

Thanks,
Catharine