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

doi:10.1002/malq.202200062

Xianglong Ruan, Xiaochuan Liu

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

Logic

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

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