# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$

Example 1.2.6.9. Let $G$ be a directed graph and let $\vec{e}$ be a morphism in the path category $\operatorname{Path}[G]$, given by a sequence of edges $(e_ n, e_{n-1}, \ldots , e_1)$ satisfying $t(e_ i) = s(e_{i+1})$. Then $\vec{e}$ is indecomposable if and only if $n=1$.