In answer to Paul Taylor

In answer to Paul Taylor

[Andree Ehresmann]

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