Editing Diffeology (section)

=== History ===
The concept of diffeology was first introduced by [[Jean-Marie Souriau]] in the 1980s under the name ''espace différentiel.''<ref name="Sour80"/><ref name="Sour84"/> Souriau's motivating application for diffeology was to uniformly handle the infinite-dimensional groups arising from his work in [[geometric quantization]]. Thus the notion of diffeological group preceded the more general concept of a diffeological space. Souriau's diffeological program was taken up by his students, particularly [[Paul G. Donato|Paul Donato]]<ref name="Don84"/> and [[Patrick Iglesias-Zemmour]],<ref name="Igl85"/> who completed early pioneering work in the field.

A structure similar to diffeology was introduced by [[Kuo-Tsaï Chen]] (陳國才, ''Chen Guocai'') in the 1970s, in order to formalize certain computations with path integrals. Chen's definition used [[convex set]]s instead of open sets for the domains of the plots.<ref name="Chen77"/> The similarity between diffeological and "Chen" structures can be made precise by viewing both as concrete sheaves over the appropriate concrete site.<ref name="BaezHof11"/>