We extend to semi-abelian categories the notion of characteristic subobject, which is widely used in group theory and in the theory of Lie algebras. Moreover, we show that many of the classical properties of characteristic subgroups of a group hold in the general semi-abelian context, or in stronger ones.
Keywords: characteristic subobject, semi-abelian categories, commutators, centralisers
2010 MSC: 17B30, 17D99, 18C05, 08A30, 08C05
Theory and Applications of Categories, Vol. 30, 2015, No. 7, pp 206-228.