Very generally, the relative point of view on a subject given by a category replaces the consideration of properties of objects of with properties of morphisms of . This is considered a generalisation, as an object is identified with the? morphism from to a terminal object of . Of course, must have a terminal object for this generalisation to be possible.
Often one will fix an object and concentrate on objects of over ; these form the over-category . The original category may be recovered as , where is a terminal object.
More generally, applying the relative point of view to category theory leads to the notion of category over a category, which is helpful for studying concrete categories (as above) as well as fibred categories.