Morita theory for quantales
Category Theory
2025-02-18 v1 Quantum Algebra
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.
Cite
@article{arxiv.2502.11795,
title = {Morita theory for quantales},
author = {Bachuki Mesablishvili},
journal= {arXiv preprint arXiv:2502.11795},
year = {2025}
}