Definition 3

The groupoid Coh($\varphi , \psi$ ) is called the cohomotopizer of the pair $(\varphi , \psi )$. One says that $\alpha$ is the canonical morphism from G into Coh($\varphi , \psi$ ) and that $h$ is the canonical homotopy joining $\alpha \circ \varphi$ to $\alpha \circ \psi$.

The quiver whose set of vertices is the set of orbits of G, whose set of arrows is the set of connected components of H, and whose origin and end mappings are deduced from $\varphi$ and $\psi$ by passing to the quotients is called the framework of the pair $(\varphi , \psi )$.