TY - GEN

T1 - Semi-galois Categories I

T2 - 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016

AU - Uramoto, Takeo

N1 - Publisher Copyright:
© 2016 ACM.

PY - 2016/7/5

Y1 - 2016/7/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84994671124&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994671124&partnerID=8YFLogxK

U2 - 10.1145/2933575.2934528

DO - 10.1145/2933575.2934528

M3 - Conference contribution

AN - SCOPUS:84994671124

T3 - Proceedings - Symposium on Logic in Computer Science

SP - 545

EP - 554

BT - Proceedings of the 31st Annual ACM-IEEE Symposium on Logic in Computer Science, LICS 2016

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 5 July 2016 through 8 July 2016

ER -