By the way, Julio: it's no big deal, but the best place for asking questions about Chapter 3 is in the discussion called [Chapter 3](https://forum.azimuthproject.org/discussion/2196/chapter-3/p1). This here is the best place for asking questions about Lecture 34, or answering puzzles from that lecture.
Sometime really soon, like in Lecture 35, I'll talk about the free category on a graph. That's what your question is really about: the difference between a graph, and the free category on that graph.
But it's much more important to ask questions than to worry about where and when to ask them! If you're puzzled by the answers so far, ask more!