Sheaf Representations and Duality in Logic

Steve Awodey

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arXiv · 2001.09195

Sheaf Representations and Duality in Logic

Steve Awodey

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Abstract

The fundamental duality theories relating algebra and geometry that were discovered in the mid-20th century can also be applied to logic via its algebraization under categorical logic. They thereby result in known and new completeness theorems. This idea can be taken even further via what is sometimes called ``categorification'' to establish a new connection between logic and geometry, a glimpse of which can also be had in topos theory.

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Steve Awodey. 2020-01-24. Sheaf Representations and Duality in Logic. https://arxiv.org/abs/2001.09195

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