Eduardo J. Dubuc

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The notion of a (pointed) Galois pretopos (“catégorie galoisienne”) was considered originally by Grothendieck in [12] in connection with the fundamental group of an scheme. In that paper Galois theory is conceived as the axiomatic characterization of the classifying pretopos of a profinite group G. The fundamental theorem takes the form of a representation(More)
It is well known that the category of covering projections (that is, locally constant objects) of a locally connected topos is equivalent to the classifying topos of a strict progroupoid (or, equivalently, a localic prodiscrete groupoid), the fundamental progroupoid, and that this progroupoid represents first degree cohomology. In this paper we generalize(More)
We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MValgebras is arithmetic, the(More)
A locally connected topos is a Galois topos if the Galois objects generate the topos. We show that the full subcategory of Galois objects in any connected locally connected topos is an inversely 2-filtered 2-category, and as an application of the construction of 2-filtered bilimits of topoi, we show that every Galois topos has a point. introduction. Galois(More)
Résumé. Nous définissons la notion de 2-catégorie 2-filtrante et donnons une construction explicite du bicolimite d’un 2-foncteur à valeurs dans les catégories. Une catégorie considérée une 2-catégorie triviale est 2-filtrante si et seulement si c’est une catégorie filtrante, et notre construction conduit à une catégorie équivalente à la catégorie qui(More)
We detected an important omission: in the definition of the category of MV-spaces (Definition 3.1), the morphisms Ff (x) φx −→ Ex should be required to be injective. Consequently f F φ −→ E amonomorphism in the topos Sh(X). The following simple counterexample was send to us by Mike Hampton. Let C be Chang’s MV-algebra (Algebraic analysis of many-valued(More)
In this article we prove the following: A topos with a point is connected atomic if and only if it is the classifying topos of a localic group, and this group can be taken to be the locale of automorphisms of the point. We explain and give the necessary definitions to understand this statement. The hard direction in this equivalence was first proved in(More)