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On the representation theory of Galois and atomic topoi
 J. Pure Appl. Algebra
"... introduction ..."
Galois Groupoids and Covering Morphisms in Topos Theory
"... The goals of this paper are (1) to compare the Galois groupoid that appears naturally in the construction of the fundamental groupoid of a topos E bounded over an arbitrary base topos S given by Bunge (1992), with the formal Galois groupoid defined by Janelidze (1990) in a very general setting given ..."
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The goals of this paper are (1) to compare the Galois groupoid that appears naturally in the construction of the fundamental groupoid of a topos E bounded over an arbitrary base topos S given by Bunge (1992), with the formal Galois groupoid defined by Janelidze (1990) in a very general setting given by a pair of adjoint functors, and (2) to discuss a good notion of covering morphism of a topos E over S which is general enough to include, in addition to the covering projections determined by the locally constant objects, also the unramified morphisms of topos theory given by those local homeomorphisms which are at the same time complete spreads in the sense of BungeFunk (1996, 1998).
2FILTEREDNESS AND THE POINT OF EVERY GALOIS TOPOS
, 801
"... Abstract. 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 2filtered 2category, and as an application of the construction of 2filtered bilimits of topo ..."
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Abstract. 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 2filtered 2category, and as an application of the construction of 2filtered bilimits of topoi, we show that every Galois topos has a point. introduction. Galois topoi (definition 1.5) arise in Grothendieck’s Galois theory of locally connected topoi. They are an special kind of atomic topoi. It is well known that atomic topoi may be pointless [6], however, in this paper we show that any Galois topos has points. We show how the full subcategory of Galois objects (definition 1.2) in any connected locally connected topos E has an structure of 2filtered 2category (in the sense of [3]). Then we show that the assignment, to each Galois object A, of the category DA of connected locally constant objects trivialized by