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How can I create a Category Index page that lists all categories?

I have themed my category.php file so it now displays all posts that belong to the category that was clicked. The URL looks like [www.example.com/category/news/]. This is good and correct.

When I go to [www.example.com/category/] I am expecting to find a Category index page that lists all created categories but I receive a 404.

I have looked in the WP Codex and have not found anything that can help me create a Category index page. Is this possible? If so how do I go about starting? Please forgive me if this has already been answered as I may not be asking the right things.

NOTE: I know that I will be using the wp_list_categories function so that is not the question.