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Extending the topological presheaf-bundle adjunction to sites and toposes

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Extending the topological presheaf-bundle adjunction to sites and toposes
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31
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CC Attribution 3.0 Unported:
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Talk at the school and conference “Toposes online” A well-known result in topology states that for any topological space X there exists an adjunction between its category of presheaves Psh(X) and the category of bundles over X, i.e. Top/X. The purpose of this talk is to extend this result by replacing X with a small site (C,J), by using the tools of fibrations and of comorphisms of sites. One particularly relevant consequence is a geometric perspective on the sheafification functor a:Psh(C) -- Sh(C,J).