# Question regarding notation in path homology paper

In the paper, https://www.math.uni-bielefeld.de/~grigor/quivers.pdf
I have two questions regarding the definitions on Page $5$.

1. What is $\sum c$ in Equation $3.1$ ? Is this just a new edge connecting the starting vertex of edge $a$ to end vertex of edge $b$ in path $[ab]$?
2. What does $N$ stand for in Equations $3.2$, and later in $3.3$? Is this a chain-complex operator?

I understand that the section of the paper that I have pasted here is not self-contained. My apologies for that.

• No, the product of arrows is not a path but a (formal) sum of arrows. Note that this is not a product on the quiver itself but on (presumably) the abelian group generated by the arrows of the quiver. – Tobias Kildetoft Sep 19 '18 at 9:50
• @TobiasKildetoft: Could you please elaborate on your answer with a small example? It would greatly help. And what about Qn 2 regarding N? – cbro Sep 19 '18 at 9:57