ok, so in the products table add a categoryID column
also create a category table to define your categories:
categoryID -Primary Key
when you run data bridge to create the products admin pages, set the category column of the products table to be a menu and use the categories table to populate it.
when you create the public product pages, include the category column in the search form, again set the category column to be a menu and use the categories table to populate it.
if you do a search for a category, you should see that the results page now uses URL variables to tell what category to show products for, use that URL in the links of your menu.