Zero morphism

In category theory, a branch of mathematics, a zero morphism is a special kind of morphism exhibiting properties like the morphisms to and from a zero object.

Dually, f is called a coconstant morphism (or sometimes right zero morphism) if for any object Z in C and any g, h : Y → Z, gf = hf.

If C is a category with zero morphisms, then the collection of 0XY is unique.

Then, gf is a zero morphism in MorC(X, Y).

If a category has zero morphisms, then one can define the notions of kernel and cokernel for any morphism in that category.