作为模块的滑轮
Sheaves as modules
摘要：
我们重新审视层的位置，把他们的背景下的Quantale模块的理论。局部同胚$p:X\to B$与希尔伯特$B$ -模是一致的，这些模具有自然的基概念。这些模的同态必然是可伴随的，由此产生的自对偶范畴给出了局部同胚与层之间等价的描述，由此层的态射作为局部同胚映射的“算子伴随”而出现。
英文摘要：
We revisit sheaves on locales by placing them in the context of the theory of quantale modules. The local homeomorphisms $p:X\to B$ are identified with the Hilbert $B$-modules that are equipped with a natural notion of basis. The homomorphisms of these modules are necessarily adjointable, and the resulting self-dual category yields a description of the equivalence between local homeomorphisms and sheaves whereby morphisms of sheaves arise as the ``operator adjoints'' of the maps of local homeomorphisms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
