THE CATEGORY OF L-ALGEBRAS

被引：0

作者：

Rump, Wolfgang ^{[1
]}

机构：

[1] Univ Stuttgart, Inst Algebra & Number Theory, Pfaffenwaldring 57, D-70550 Stuttgart, Germany

来源：

THEORY AND APPLICATIONS OF CATEGORIES | 2023年 / 39卷 / 21期

关键词：

L-algebra; regular category; Barr-exact; protomodular; semidirect product; SEMIDIRECT PRODUCTS; GARSIDE GROUPS; MV-ALGEBRAS; MONOIDS; IDEALS; THEOREM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The category LAlg of L-algebras is shown to be complete and cocomplete, regular with a zero object and a projective generator, normal and subtractive, ideal determined, but not Barr-exact. Originating from algebraic logic, L-algebras arise in the theory of Garside groups, measure theory, functional analysis, and operator theory. It is shown that the category LAlg is far from protomodular, but it has natural semidirect products which have not been described in category-theoretic terms.

引用

页码：598 / 624

页数：27

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