Semi-galois Categories I: The Classical Eilenberg Variety Theory

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


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 Eilenbergtype 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 semigalois categories.

Original languageEnglish
Title of host publicationProceedings of the 31st Annual ACM-IEEE Symposium on Logic in Computer Science, LICS 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages10
ISBN (Electronic)9781450343916
Publication statusPublished - Jul 5 2016
Externally publishedYes
Event31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016 - New York, United States
Duration: Jul 5 2016Jul 8 2016

Publication series

NameProceedings - Symposium on Logic in Computer Science
ISSN (Print)1043-6871


Other31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016
Country/TerritoryUnited States
CityNew York

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)


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