Normalities and commutators (Q618264)

Both in universal algebra and in category theory, there is a number of papers extending the concepts of a normal subobject and a commutator from groups to more general categories. The paper contributes to this endeavour. A new notion of normality is defined using Higgins' commutator. The main result extends the well-known characterization of a normal subgroup \(K\) in \(A\) by means of the commutator \([A,K]\) from groups to semi-abelian categories.