On the normality of Higgins commutators

• Alan S. Cigoli ^[1] ; James R.A. Gray ^[2] ; Tim Van der Linden ^[3]
  1. [1] University of Milan

     University of Milan

     Milán, Italia

     
  2. [2] Stellenbosch University

     Stellenbosch University

     Stellenbosch, Sudáfrica

     
  3. [3] Université Catholique de Louvain

     Université Catholique de Louvain

     Arrondissement de Nivelles, Bélgica

     

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• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 4 ((April 2015) ), 2015, págs. 897-912
• Idioma: inglés
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• Resumen

  • In a semi-abelian context, we study the condition (NH) asking that Higgins commutators of normal subobjects are normal subobjects. We provide examples of categories that do or do not satisfy this property. We focus on the relationship with the Smith is Huq condition (SH) and characterise those semi-abelian categories in which both (NH) and (SH) hold in terms of reflection and preservation properties of the change of base functors of the fibration of points.