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.
On the “Smith is Huq” Condition in S-Protomodular Categories / N. Martins Ferreira, A. Montoli. - In: APPLIED CATEGORICAL STRUCTURES. - ISSN 0927-2852. - 25:1(2017 Feb 01), pp. 59-75. [10.1007/s10485-015-9411-1]
On the “Smith is Huq” Condition in S-Protomodular Categories
A. Montoli
2017
Abstract
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.
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