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arXiv · 2605.22071

Duality theory for categorical theories

Lingyuan Ye
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Abstract

We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids. We also study the geometry of profinite monoids via the classifying topos construction, and show it identifies them as a full sub-2-category of the 2-category of topoi.

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Lingyuan Ye. 2026-05-21. Duality theory for categorical theories. https://arxiv.org/abs/2605.22071

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