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A category (in a wiki often called namespace) is under normal circumstances known as the first part of the page name - the partial name before the colon (:) in the page name. You will see this page name in the adress bar as the last part of the URL. This is NOT PART of the page title!
A page name without such colon in its name belongs in wikidot.com to the "_default" category.
It is possible to make the content of pages of a specified category "private" and visible only to specified groups of visitors. In your _admin site manager page you will see a "View" row in the "Permissions" section . You will only see this for categories that are not the _default category.
You will need to create a landing page for visitors without the View permission. That landing page should be called category:_public.