There are a few ways to go about this.
the simplest would be to use Data Bridge to create a Search results page, set the search up to search for categories
use an example search as a starting place for creating the links you will need, you will notice when you do a search, it will create URL variables to pass the category yo u searched form and a trigger variable to the results page, similar to this:
results.php?Category=Lectures&Search=Search
for your menu, create a recordset to return the categories, then use a repeat region to write the categories to the page and inlcude links that pass the category similar to the example.
