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Operator algebras from toposes

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Operator algebras from toposes
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25
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28
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CC Attribution 3.0 Unported:
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Abstract: Grothendieck Toposes and $C^*$-algebras are two distinct generalizations of the concept of topological space and there is a lot of examples of objects to which one can attach both a topos and a $C^*$-algebra in order to study there properties: dynamical systems, foliations, Graphs, Automaton, topological groupoids etc. It is hence a natural question to try to understand the relation between these two sort different object. In this talk I will explain how to attach $C^*$-algebras and Von Neuman al gebras to (reasonable) toposes, in a way that recover the $C^*$-algebra attached to all the above examples.