Very generally, the relative point of view on a subject given by a category$C$ replaces the consideration of properties of objects of $C$ with properties of morphisms of $C$. This is considered a generalisation, as an object $x$ is identified with the? morphism from $x$ to a terminal object of $C$. Of course, $C$ must have a terminal object for this generalisation to be possible.

Often one will fix an object $y$ and concentrate on objects of $C$over$y$; these form the over-category$C/y$. The original category $C$ may be recovered as $C/1$, where $1$ is a terminal object.