In a category , a constant morphism satisfies for any and ,
whereas a coconstant morphism satisfies for any .
A zero morphism is both a constant and coconstant morphism. cat
A category is said to have zero morphisms iff for any two objects there is a fixed morphism such that the following diagram commutes cat
for any and .
Properties
A category with zero morphisms allows one to define the Kernels and cokernels of morphisms.