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GIUSEPPE METERE

Normalities and commutators

  • Authors: Mantovani, S.; Metere, G.
  • Publication year: 2010
  • Type: Articolo in rivista (Articolo in rivista)
  • Key words: Normal subobject; Ideal; Commutator; Semi-abelian

Abstract

We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of this commutator. Our main result is to extend to any semi-abelian category the following well-known characterization of normal subgroups: a subobject K is normal in A if. and only if, {[A, K] <= K. (C) 2010 Elsevier Inc. All rights reserved.}