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On formal theory of differential equations. III. (English) Zbl 0728.58041
The paper continues the author’s investigations on so-called diffieties (the infinite prolongations of general systems of PDE) [see part I, II of this paper, Čas. Pěstování Mat. 111, 353-383 (1986; Zbl 0638.35008), ibid. 114, 60-105 (1989; Zbl 0703.34001)]; the aim is to develop the elements of general theory of Lie-Cartan pseudogroups with regard of the fact that the study of pseudogroups with the help of diffieties is independent of any particular realization by transformations of a geometrical object. The relations with the equivalence problem, theory of geometrical objects and connection theory are briefly discussed.

58H05 Pseudogroups and differentiable groupoids
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
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