Catégories inductives et pseudogroupes. (French) Zbl 0099.26002

Summary: The author goes again over the ground covered in his previous article [Jahresber. Dtsch. Math.-Ver. 60, 49–77 (1957; Zbl 0097.37803)] in an even more abstract fashion. The treatment, based on “induction functors” which generate an order relation in a certain type of groupoids, seems to avoid most logical difficulties, except those intrinsically connected with the notion of category. It is rather difficult to judge the importance of the changes introduced in this latest edition of the theory of jets until the long promised detailed study of Lie pseudogroups will have appeared.
Reviewer: H. Guggenheimer


18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
20N05 Loops, quasigroups
58A20 Jets in global analysis


Zbl 0097.37803
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[1] [1] , Gattungen von lokalen Strukturen (Jahresbericht der Deutschen Math. Vereinigung, 60, 1957, p. 49-77). · Zbl 0097.37803
[2] [2] Catégories topologiques et catégories différentiables (Colloque Geométrie Différentielle Globale, Bruxelles, 1958 CBRM). · Zbl 0205.28202
[3] [3] Introduction à la théorie des structures infinitésimales et des pseudo-groupes de Lie (Colloque Int. de Géométrie diff. de Strasbourg, C.N.R.S., 1953). · Zbl 0053.12002
[4] [4] Grupoides diferenciables y pseudogrupos de Lie (Revista Union Mat. Argentina, 1960, vol XIX, p. 48).
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