This is an expository paper in which we explain the basic ideas of topos theory in connection with semigroup theory. We focus mainly on the classifying topos of an inverse semigroup or pseudogroup, and to some extent on creating a dictionary between the language of semigroups and topos theory. We begin with the algebraic theory having to do with inverse semigroups, and then turn to an analysis of pseudogroups using sheaf theory. Our work includes some new material on wide semigroup homomorphisms and their geometric morphisms.

中文翻译：

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Toposes for semigroups: 邀请

这是一篇说明性论文，我们在其中解释了与半群理论相关的拓扑理论的基本思想。我们主要关注逆半群或伪群的拓扑分类，并在某种程度上创建了半群语言和拓扑理论之间的字典。我们从与逆半群有关的代数理论开始，然后转向使用层理论分析伪群。我们的工作包括一些关于宽半群同态及其几何态射的新材料。