In answer to Paul Taylor Charles Ehresmann has realized as soon as 1951 (cf. "Charles Ehresmann: Oeuvres complètes et commentées", Part I, p. 153) that in a pseudogroup of transformations only the open sets of the associated topology are used, not the points, whence the idea of replacing the pseudogroup of transformations by a groupoid and the topology by a paratopology (i.e., a complete distributive lattice). He formalized this idea in later works, in particular in the 1957 seminal paper "Gattungen von lokalen Strukturen" [Oeuvres, Part II, p. 126], where he replaces the pseudogroup of transformations by a local groupoid, and even, more generally, by a local category, that is a category equipped with a "local" order compatible with its structure (in modern term it is a category internal to a category of locales); and he develops the theory of complete local species of structures over a local groupoid, which generalizes that of a sheaf. Andrée