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

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Martins-Ferreira, Nelson Montoli, Andrea [UCL]

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2015
Language Anglais
Journal information "Applied Categorical Structures : a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science" - (2015)
Peer reviewed yes
Publisher Springer Netherlands (Dordrecht)
issn 0927-2852
e-issn 1572-9095
Publication status Accepté/Sous presse
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Keywords Huq commuting morphisms ; Monoids with operations ; S-protomodular categories ; Schreier split epimorphisms ; Smith-Pedicchio centralising relations
Links
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Bibliographic reference Martins-Ferreira, Nelson ; Montoli, Andrea. On the “Smith is Huq” Condition in S-Protomodular Categories. In: Applied Categorical Structures : a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science, (2015)
Permanent URL http://hdl.handle.net/2078.1/173368