In category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of 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.
[citation needed] On the other hand, every epimorphism in the category of groups is conormal (since it is the cokernel of its own kernel), so this category is conormal.
In an abelian category, every monomorphism is the kernel of its cokernel, and every epimorphism is the cokernel of its kernel.