论文标题
埃塔尔覆盖的群体的作用
Actions of étale-covered groupoids
论文作者
论文摘要
通过仅限于一类本地开放式群体$ g $，与lie groupoid类似，它具有适当的覆盖范围$ \ widehat g \ toétalegroupoids，我们扩展了有关以前证明的to groupoidsoids的群体动作和量化的结果，但似乎对派遣了典型的开放式群体，但对任意开放的群体无效。特别是，我们获得了$ g $ actions类别作为$ \ MATHCAL O（\ wideHat G）$的量子模块类别的表征，该量子模块满足了与量子$ \ MATHCAL O（g）$相关的条件。这导致了$ g $ sheaves的简单描述和$ g $的分类$ g $在hilbert $ \ mathcal o（\ widehat g）$ - 模块方面。 1细胞是群体双重运动的生物学与相应的量子和双模型的生物相等。
By restricting to a class of localic open groupoids $G$ which, similarly to Lie groupoids, possess appropriate covers $\widehat G\to G$ by étale groupoids, we extend results about groupoid actions and quantales that were previously proved for étale groupoids but do not seem to work for arbitrary open groupoids. In particular we obtain a characterization of the category of $G$-actions as a category of quantale modules on $\mathcal O(\widehat G)$ that satisfy a condition related to the quantale $\mathcal O(G)$. This leads to a simple description of $G$-sheaves and the classifying topos of $G$ in terms of Hilbert $\mathcal O(\widehat G)$-modules. The bicategory whose 1-cells are the groupoid bi-actions is bi-equivalent to a corresponding bicategory of quantales and bimodules.
