We take advantage of the correspondence between pseudogroups and inverse quantal frames, and of the recent description of Morita equivalence for inverse quantal frames in terms of biprincipal bisheaves, to define Morita equivalence for pseudogroups and to investigate its applications. In particular, two pseudogroups are Morita equivalent if and only if their corresponding localic étale groupoids are. We explore the clear analogies between our definition of Morita equivalence for pseudogroups and the usual notion of strong Morita equivalence for $C^{⁎}$-algebras and these lead to a number of concrete results.

中文翻译：

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伪群的森田等价

我们利用伪群和逆量子框架之间的对应关系，以及最近根据双主双叶对逆量子框架 Morita 等价的描述，来定义伪群的 Morita 等价并研究其应用。特别地，两个伪群是 Morita 等价的当且仅当它们对应的局部 étale groupoids 是。我们探索了我们对伪群的森田等价的定义与通常的强森田等价概念之间的明显类比$C^{⁎}$-代数和这些导致了一些具体的结果。