Category theory MOC

Zero morphism

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. #m/def/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 #m/def/cat

for any and .

Properties

• A category with zero morphisms allows one to define the Kernels and cokernels of morphisms.

#state/tidy | #lang/en | #SemBr