Martins-Ferreira, NelsonMontoli, Andrea2025-10-022025-10-022017-02Martins-Ferreira, N., Montoli, A. On the “Smith is Huq” Condition in S-Protomodular Categories. Appl Categor Struct 25, 59–75 (2017). https://doi.org/10.1007/s10485-015-9411-10927-28521572-9095http://hdl.handle.net/10400.8/14197We 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.engSmith-Pedicchio centralising relationsHuq commuting morphismsS-protomodular categoriesMonoids with operationsSchreier split epimorphismsjournal article10.1007/s10485-015-9411-1