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

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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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Authors and Affiliations

  1. ESTG, CDRSP, Instituto Politécnico de Leiria, Leiria, Portugal

    Nelson Martins-Ferreira

  2. CMUC, University of Coimbra, 3001-501, Coimbra, Portugal

    Andrea Montoli

  3. Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, chemin du Cyclotron 2 bte L7.01.02, 1348, Louvain-la-Neuve, Belgium

    Andrea Montoli

Authors
  1. Nelson Martins-Ferreira
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  2. Andrea Montoli
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Correspondence to Andrea Montoli.

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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

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  • DOI: https://doi.org/10.1007/s10485-015-9411-1

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