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A category is an admin level tag. This means that only users with administrative rights or write access can assign articles to categories while readers can not.
Categories make it possible to group articles in different sections in one location. Unlike sections, an article can be assigned to more then one category. This allows you to filter, group and even search content in a section.
You can either do this when you first create the article or at a later time by editing the options for an article.