## Diagrammes localement libres, extensions de corps et théorie de Galois.(French)Zbl 0569.18001

Diagrammes 10, L1-L17 (1983).
The notion of a ”locally free diagram” $$\delta$$ : $${\mathcal D}\to {\mathcal A}$$ has been defined by the author [cf. ibid. 9, Exp. No.1 (1983; Zbl 0521.18012)]. In the present paper some sufficient conditions are stated under which two locally free diagrams in the category $${\mathcal A}$$ over an object B of a category $${\mathcal B}$$ are isomorphic. E.g., this is the case if $${\mathcal D}$$ is discrete or $${\mathcal D}$$ is a group. By means of a special functor from a complete semilattice to the category Cat the notions of pre-Galois and Galois categories and the locally free diagrams over B are defined. For such diagrams the uniqueness up to isomorphism is proved, too. Some theorems on the existence of locally free diagrams of a given type over B are stated (e.g. if $${\mathcal B}$$ is the category of fields).
Reviewer: M.Sekanina

### MSC:

 18A10 Graphs, diagram schemes, precategories 20J99 Connections of group theory with homological algebra and category theory 12F10 Separable extensions, Galois theory 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)

Zbl 0521.18012
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