论文标题
概括典型的类固醇 - 完全伪群对应
Generalising the étale groupoid--complete pseudogroup correspondence
论文作者
论文摘要
我们证明，由于重新构成和lawson-lenz的概括，我们的替代类固醇之间是拓扑组的，其源地图是局部同构的同构---完整的伪群 - - 与单型相反的单体相反，它们在拓扑空间上具有特别好的表现形式。 我们的概括以四种方式改善了现有功能通信。首先，我们扩大了在每一侧出现的地图类别。其次，我们从逆类别的一侧概括到一侧到反类别，而在另一侧，从étalegropsoids到我们所谓的partiteétaleglopoids。第三，我们从étalegrassoids概括到源étale类别，而在另一侧，从逆肌逆转到限制单体。第四，而且最远见的是，我们从拓扑典型的类固定概括到带有局部胶水的任何联接限制类别C的内部内部的odtale groupoid； and on the other side, from complete pseudogroups to ``complete C-pseudogroups'', i.e., inverse monoids with a nice representation on an object of C. Taken together, our results yield an equivalence, for a join restriction category C with local glueings, between join restriction categories with a well-behaved functor to C, and partite source-étale internal categories in C. In fact, we obtain this by cutting down a larger c的任意限制类别与C的partite内部类别之间的邻接。 除了证明这一主要结果外，还提供了许多应用程序，这些应用程序重建并扩展了文献中的现有信件，并提供了完成过程的一般公式。
We prove a generalisation of the correspondence, due to Resende and Lawson--Lenz, between étale groupoids---which are topological groupoids whose source map is a local homeomorphisms---and complete pseudogroups---which are inverse monoids equipped with a particularly nice representation on a topological space. Our generalisation improves on the existing functorial correspondence in four ways. Firstly, we enlarge the classes of maps appearing to each side. Secondly, we generalise on one side from inverse monoids to inverse categories, and on the other side, from étale groupoids to what we call partite étale groupoids. Thirdly, we generalise from étale groupoids to source-étale categories, and on the other side, from inverse monoids to restriction monoids. Fourthly, and most far-reachingly, we generalise from topological étale groupoids to étale groupoids internal to any join restriction category C with local glueings; and on the other side, from complete pseudogroups to ``complete C-pseudogroups'', i.e., inverse monoids with a nice representation on an object of C. Taken together, our results yield an equivalence, for a join restriction category C with local glueings, between join restriction categories with a well-behaved functor to C, and partite source-étale internal categories in C. In fact, we obtain this by cutting down a larger adjunction between arbitrary restriction categories over C, and partite internal categories in C. Beyond proving this main result, numerous applications are given, which reconstruct and extend existing correspondences in the literature, and provide general formulations of completion processes.
