The notion of a normal subobject is the proper generalization of a normal subgroup to other algebraic categories. The notion was found relatively late. In the category of groups, there are two equivalent descriptions of a normal subgroup: as the kernel of a homomorphism of groups and as the equivalence class of the unit of some (necessarily unique) congruence.
Given a category admitting finite limits, one says that a morphism in is normal to the internal equivalence relation if it factors through the monomorphism (i.e. such that and …)
A normal subobject is a monomorphism which is normal to some equivalence relation.
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A protomodular category is defined in such a way that it possesses an intrinsic notion of normal subobject.
See also normal monomorphism
Last revised on August 16, 2016 at 14:48:53. See the history of this page for a list of all contributions to it.