Categories are basically a backlink from a Page. (i.e. when answering "what links here" a Dog could be back-linked to an Animal)

A Page inside of a Category might have a special relationship with that category, perhaps it's related to the category, perhaps it fits squarely inside, perhaps it's an opposing idea but necessary to understand the full context of the other objects in the category.

Perhaps then the Category object isn't useful? Perhaps the way of "categorizing" something would be to write about it in another page, and you could see the backlinks.

Animation to reveal backlinks