2025/02/17 by Mesablishvili, Bachuki
#18B25 #18C15 #18C20 #18D20 #18E08 #18F10 #18F75 #18M05 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2502.11795
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.