Concept# Normal morphism

Summary

In and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of morphism.
A normal category is a category in which every monomorphism is normal. A conormal category is one in which every epimorphism is conormal.
Definition
A monomorphism is normal if it is the of some morphism, and an epimorphism is conormal if it is the of some morphism.
A category C is binormal if it's both normal and conormal.
But note that some authors will use the word "normal" only to indicate that C is binormal.
Examples
In the , a monomorphism f from H to G is normal if and only if its image is a normal subgroup of G. In particular, if H is a subgroup of G, then the inclusion map i from H to G is a monomorphism, and will be normal if and only if H is a normal subgroup of G. In fact, this is the origin of the term "normal" for monomorphisms.
On the other hand, every epimorphism in the category of groups is conormal (since it i

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