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arXiv · 2502.11795

Morita theory for quantales

Bachuki Mesablishvili
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Abstract

Morita theory for quantales is developed. The main result of the paper is a characterization of those quantaloids (categories enriched in the symmetric monoidal closed category of sup-lattices) that are equivalent to modular categories over quantales. Based on this characterization, necessary and sufficient conditions are derived for two quantales to be Morita-equivalent, i. e. have equivalent module categories. As an application, it is shown that the category of internal sup-lattices in a Grothendieck topos is equivalent to the module category over a suitable chosen ordinary quantale.

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Bachuki Mesablishvili. 2025-02-17. Morita theory for quantales. https://arxiv.org/abs/2502.11795

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