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arXiv · 1002.1372

Normalities and Commutators

Sandra Mantovani·Giuseppe Metere
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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, $[A,K]\leq K$.

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Sandra Mantovani, Giuseppe Metere. 2010-02-08. Normalities and Commutators. https://arxiv.org/abs/1002.1372

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