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首页> 外文会议>Annual ACM/IEEE Symposium on Logic in Computer Science >Semi-galois Categories I: The Classical Eilenberg Variety Theory
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Semi-galois Categories I: The Classical Eilenberg Variety Theory

机译：半伽罗瓦类别I：古典艾伦伯格多样性理论

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Recently, Eilenberg's variety theorem was reformulated in the light of Stone's duality theorem. On one level, this reformulation led to a unification of several existing Eilenberg-type theorems and further generalizations of these theorems. On another level, this reformulation is also a natural continuation of a research line on profinite monoids that has been developed since the late 1980s. The current paper concerns the latter in particular. In this relation, this paper introduces and studies the class of semi-galois categories, i.e. an extension of galois categories; and develops a particularly fundamental theory concerning semi-galois categories: That is, (I) a duality theorem between profinite monoids and semi-galois categories; (II) a coherent duality-based reformulation of two classical Eilenberg-type variety theorems due to Straubing [30] and Chaubard et al. [10]; and (III) a Galois-type classification of closed subgroups of profinite monoids in terms of finite discrete cofibrations over semi-galois categories.
机译：最近，根据斯通的对偶定理，重新定义了艾伦伯格的变分定理。在某种程度上，这种重新表述导致了几个现有的Eilenberg型定理的统一以及这些定理的进一步推广。在另一个层面上，这种重新定义也是自1980年代后期以来发展的关于有限mono半体的研究路线的自然延续。当前的论文特别涉及后者。在这种关系中，本文介绍并研究了半伽罗瓦类别的类别，即伽罗瓦类别的扩展;并发展出一种关于半伽罗瓦类别的特别基础的理论：（I）有限mono半群与半伽罗瓦类别之间的对偶定理; （II）由于Straubing [30]和Chaubard等人，两个经典的Eilenberg型变异定理基于一致对偶性的重新表述。 [10]; （III）在半伽罗瓦类别上的有限离散共成纤维作用下，有限半id半身的封闭子群的伽罗瓦型分类。

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