Étale groupoids as germ groupoids and their base extensions
Étale groupoids as germ groupoids and their base extensions
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Étale groupoids 作为胚芽 groupoids 及其基础扩展
DOI：
10.1017/s001309150800076x
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发表时间：
2008
影响因子：
0.7
通讯作者：
P. Resende
中科院分区：
文献类型：
--
作者：
D. Matsnev;P. Resende
本文引入了逆半群的广表示的概念，并证明了在适当定义的拓扑下，存在一个这种表示的芽空间，该芽空间具有Etale广群胚的结构。这给出了一个优雅的描述帕特森的普遍广群和翻译广群的Skandalis，涂和余。此外，我们的特点，逆半群所产生的群胚，导致一个精确的双射类的étale群胚和类的完整的和无限分配的逆幺半群配备适当的表示，我们解释的意义，其中quantales和局部群胚进行推广这种对应。
Abstract We introduce the notion of wide representation of an inverse semigroup and prove that with a suitably defined topology there is a space of germs of such a representation that has the structure of an étale groupoid. This gives an elegant description of Paterson's universal groupoid and of the translation groupoid of Skandalis, Tu and Yu. In addition, we characterize the inverse semigroups that arise from groupoids, leading to a precise bijection between the class of étale groupoids and the class of complete and infinitely distributive inverse monoids equipped with suitable representations, and we explain the sense in which quantales and localic groupoids carry a generalization of this correspondence.