In a category π’, a constant morphismπβπ’(π,π) satisfies ππ=ππ for any π,πβπ’(π,π) and πβπ’,
whereas a coconstant morphismπβπ’(π,π) satisfies ππ=ππ for any π,πβπ’(π,π).
A zero morphism is both a constant and coconstant morphism. cat
A category π’ is said to have zero morphisms iff for any two objects π,πβπ’ there is a fixed morphism 0ππβπ’(π,π) such that the following diagram commutes cat
for any π,πβπ’ and π,πβπ’(π,π).
Properties
A category with zero morphisms allows one to define the Kernels and cokernels of morphisms.