Extension of the Galois Theory of Grothendieck.

Intro -- Table of Contents -- Introduction -- Chapter I - Sup-lattices -- 1. Definitions and duality -- 2. Limits and colimits -- 3. Free sup-lattices -- 4. Sub and quotient lattices -- 5. Tensor products -- Chapter II - Rings, modules and descent -- 1. Rings and modules -- 2. Tensor product of modules -- 3. Change of rings -- 4. Flatness, projectivity, and purity -- 5. Descent theory for modules -- Chapter III - Locales -- 1. Locales and commutative monoids -- 2. Limits and colimits -- 3. The free locale -- 4. Local operators and quotients -- 5. The splitting locale -- Chapter IV - Spaces -- 1. Subspaces -- 2. Points and discrete spaces -- 3. The Sierpinski space -- 4. Pullbacks and projective limits -- 5. The splitting space -- Chapter V - Open maps of spaces -- 1. Open maps - definition -- 2. Open subspaces -- 3. Conditions for openness -- 4. Open surjections, pullbacks -- 5. A characterization of discrete spaces -- Chapter VI - Change of base -- 1. Change of base for sup-lattices and locales -- 2. Determination of sl(S-[sup(Aop)] ) and loc(S-[sup(Aop)] ) -- 3. Determination of sl(sh(A)) and loc(sh(A)) for A ε loc(S) -- 4. The Beck-Chevalley conditions -- 5. The spatial reflection -- Chapter VII - Open morphisms of topoi -- 1. Open geometric morphisms -- 2. A site characterization of openness -- 3. The spatial cover -- 4. A characterization of atomic topoi -- Chapter VIII - Descent morphisms of topoi -- 1. Effective descent morpnisms -- 2. Open surjections -- 3. Applications to the structure of topoi -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.