Zero morphism

Summary

A zero morphism is a distinguished morphism between two objects that behaves like multiplication by zero. Composing it with any morphism on either side gives again a zero morphism. In a category with a zero object, the zero morphism $X \to Y$ is the composite $X \to 0 \to Y$. Zero morphisms are needed to define kernels and cokernels, and they make sense of the statement that a composite is zero.