On the space of morphisms between étale groupoids
arXiv:0707.4673
Abstract
Given 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 proofs