It sounds more like a friendship, maybe big sister-little sister dynamic.
Within the contexts of a friendship, this would not be considered dependency, but more so an unbalanced relationship with little reciprocity in action from Cats, though the T may receive personal satisfaction in return for helping Cats.
Cats may sometimes behave as a child, as the T claims, but it seems to me, on the comments of this thread alone, that the T treats Cats as a younger sister/friend.