You would have to add the categories yourself to the archives page.
One sort of mindless/easy way would be to get yourself a test blog (private) and export your real blog to it. Choose a theme which lists titles of posts on category pages: http://wpbtips.wordpress.com/2009/03/25/full-posts-in-archive-pages/
View the source code, and copy the list of titles (one cat at a time) then paste the html into a page for that cat on your real blog.
You’ll have an archive of posts by category on that page.
You’ll have to update the list each time you make a post.