So, I'm rather new to category theory (well, Abstract Algebra in general as well), so I decided to pick up Paulo Aluffi's "Algebra: Chapter 0". However, there is one example in the introductory chapter to Categories that I don't quite understand. He's attempting to construct a slice category $C_{A,B}$ in the following way:
Let $C$ be a given category, and let $A$ and $B$ be objects of $C$. Then, he constructs a category $C_{A,B}$ by specifying that the objects of $C_{A,B}$ will be diagrams (see picture below), and that the morphisms of $C_{A,B}$ will be commutative diagrams
My question is, based off of the diagrams he has given, how are the morphisms of $C_{A,B}$ commutative diagrams? My understanding was that a commutative diagram had to have all paths essentially going to the same place, but clearly in the the diagram Aluffi has given us, there are paths going to object $A$ and object $B$ of category $C$. Could someone please clarify this?