On the “Smith is Huq” Condition in S-Protomodular Categories

Martins-Ferreira, Nelson; Montoli, Andrea

http://hdl.handle.net/10400.8/14197

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Authors

Martins-Ferreira, Nelson

Montoli, Andrea

Abstract(s)

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.

Keywords

Smith-Pedicchio centralising relations Huq commuting morphisms S-protomodular categories Monoids with operations Schreier split epimorphisms

URI

http://hdl.handle.net/10400.8/14197

Citation

Martins-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/s10485-015-9411-1