A categorical equivalence between logical quantale modules and quantum B‐modules

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Mathematical Logic Quarterly (forthcoming)
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Abstract

This paper introduces the notion of logical quantale module. It proves that there is a dual equivalence between the category of logical quantale modules and the category of quantum B‐modules, in the way that every quantum B‐module admits a natural embedding into a logical quantale module, the enveloping quantale module.

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10.1002/malq.202200062

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Non-commutative logical algebras and algebraic quantales.Wolfgang Rump & Yi Chuan Yang - 2014 - Annals of Pure and Applied Logic 165 (2):759-785.
Quantum B‐modules.Xia Zhang & Wolfgang Rump - 2022 - Mathematical Logic Quarterly 68 (2):159-170.

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