Abstract
In this paper, based on a complete residuated lattice L, we introduce the definitions of L-quantum spaces and continuous mappings. Then we establish an adjunction between the category of stratified L-quantum spaces and the opposite category of two-sided L-quantales. We also prove that the category of sober L-quantum spaces is dually equivalent to the category of spatial two-sided L-quantales.
摘要
创新点
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(1)
本文将量化的思想应用于量子空间, 提出了L-量子空间概念, 它可以看作是非交换的L-拓扑空间。
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(2)
给出了L-量子空间上连续映射的概念, 探讨了它的一些性质。
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(3)
研究了L-量子空间的一些范畴性质, 比如 : L-量子空间范畴可以与双侧L-quantale范畴之间建立伴随。
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(4)
得到了Sober L-量子空间范畴的一个等价范畴, 即空间式的双侧L-quantale范畴。
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Zhao, B., Ma, N. L-quantum spaces. Sci. China Inf. Sci. 59, 32201 (2016). https://doi.org/10.1007/s11432-015-5416-5
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DOI: https://doi.org/10.1007/s11432-015-5416-5