2013/12/31 by Alan S. Cigoli, James Richard Andrew Gray, James R. A. Gray +1 · 1 citation
Mathematics · #Abelian group #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Context (archaeology) #Epistemology #Fibration #Focus (optics) #Functor #Geography #Homotopy and Cohomology in Algebraic Topology #Mathematics #Normality #Property (philosophy) #Pure mathematics #Statistics #math.CT #msc:08C05 #msc:17A99 #msc:18G50 #msc:20F12
paper · pdf · doi:10.1016/j.jpaa.2014.05.025
published as J. Pure Appl. Algebra 219 (2015) 897-912 · 15 pages; final published version
arxiv created 2014/04/04 · openalex publication_date 2014/05/16 · arxiv updated 2015/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.