Proposition 2

The groupoid Coh($\varphi , \psi$ ) is generated by the subquiver whose set of vertices is Som(G) and whose set of arrows is the union of the images of the mappings Fl($\alpha$ ) and $h$.

This subquiver being the image of the quiver $G_1$ under the quiver morphism $\pi \circ \theta_1$, the proposition follows at once from the construction of Coh($\varphi , \psi$ ).