Étale逆半群-基本原理
Étale inverse semigroupoids - the fundamentals
摘要：
在这篇文章中，我们将研究半群，更具体地说，逆半群。这些是逆半群和群胚的共同推广，并提供了一种自然语言，可以描述几种类型的动力学结构。此外，这个理论使我们能够精确地比较和同时推广逆半群和群胚理论的各个方面。我们首先比较和解决两个概念之间的差异半群出现在文献中（一个由蒂尔森和另一个由埃克塞尔）。我们专门研究逆半群，特别是一个类似的Vagner-Preston定理。这个表示定理引出了作用的自然概念，更一般地引出了étale逆半群胚的$\land$ -预作用和部分作用，它们推广了逆半群的拓扑作用和étale群胚的连续作用。逆半群和群胚理论中常见的许多构造也被推广，它们的范畴性质也被明确化。我们完成这篇论文的一个版本的非交换斯通对偶充分逆半群，它利用了几个上述的建设。
英文摘要：
In this article we will study semigroupoids, and more specifically inverse semigroupoids. These are a common generalization to both inverse semigroups and groupoids, and provide a natural language on which several types of dynamical structures may be described. Moreover, this theory allows us to precisely compare and simultaneously generalize aspects of both the theories of inverse semigroups and groupoids. We begin by comparing and settling the differences between two notions of semigroupoids which appear in the literature (one by Tilson and another by Exel). We specialize this study to inverse semigroupoids, and in particular an analogue of the Vagner-Preston Theorem is obtained. This representation theorem leads to natural notions of actions, and more generally $\land$-preactions and partial actions, of étale inverse semigroupoids, which generalize topological actions of inverse semigroups and continuous actions of étale groupoids. Many constructions which are commonplace in the theories of inverse semigroups and groupoids are also generalized, and their categorical properties made explicit. We finish this paper with a version of non-commutative Stone duality for ample inverse semigroupoids, which utilizes several of the aforementioned constructions.
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