On the "Smith is Huq" Condition in S-Protomodular Categories

被引：12

作者：

Martins-Ferreira, Nelson ^{[1
]}

Montoli, Andrea ^{[2
,3
]}

机构：

[1] Inst Politecn Leiria, CDRSP, ESTG, Leiria, Portugal

[2] Univ Coimbra, CMUC, P-3001501 Coimbra, Portugal

[3] Catholic Univ Louvain, Inst Rech Math & Phys, Chemin Cyclotron 2 Bte L7-01-02, B-1348 Louvain La Neuve, Belgium

来源：

APPLIED CATEGORICAL STRUCTURES | 2017年 / 25卷 / 01期

关键词：

Smith-Pedicchio centralising relations; Huq commuting morphisms; S-protomodular categories; Monoids with operations; Schreier split epimorphisms; CROSSED-MODULES; SEMIDIRECT PRODUCTS;

D O I：

10.1007/s10485-015-9411-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the so-called "Smith is Huq" condition in the context of S-protomodular categories: two S-equivalence relations centralise each other if and only if their associated normal subobjects commute. We prove that this condition is satisfied by every category of monoids with operations equipped with the class S of Schreier split epimorphisms. Some consequences in terms of characterisation of internal structures are explored.

引用

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页码：59 / 75

页数：17

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