We characterize the left-handed noncommutative frames that arise from sheaves on topological spaces. Further, we show that a general left-handed noncommutative frame $A$ arises from a sheaf on the dissolution locale associated to the commutative shadow of $A$. Both constructions are made precise in terms of dual equivalences of categories, similar to the duality result for strongly distributive skew lattices in arXiv:1206.5848.

中文翻译：

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非交换框架的对偶性

我们描述了从拓扑空间上的滑轮产生的左手非交换框架。此外，我们证明了一般的左手非交换框架 $A$ 来自与 $A$ 的交换阴影相关联的溶解区域上的一个层。两种构造都在类别的对偶等价方面进行了精确处理，类似于 arXiv:1206.5848 中强分布斜格的对偶结果。