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A topos-theoretic approach to Stone-type dualities

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We present an abstract topos-theoretic machinery for building Stone-type dualities; five known dualities are recovered as applications of our machinery to specific sets of inputs, and several new dualities are introduced. We also discuss how our topos-theoretic interpretation can be exploited to obtain results connecting properties of preorders and properties of the corresponding locales or topological spaces, and we indicate how adjunctions between various kinds of categories can be established as natural applications of our general methodology.

This talk is part of the Category Theory Seminar series.

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