2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169261Given two étale groupoids $\Cal G$ and $\Cal G'$, we consider the set of pointed morphisms from $\Cal G$ to $\Cal G'$. Under suitable hypothesis we introduce on this set a structure of Banach manifold which can be considered as the space of objects of an étale groupoid whose space of orbits is the space of morphisms from $\Cal G$ to $\Cal G'$.Amstex, 12 pages. In this revised version, we correct paragraph IV.4, add references and more details on the proofsGeometric Topologytext