morphism

monomorphism

A morphism is called a monomorphism if, for every object and all morphisms , the following holds.

epimorphism

A morphism is called an epimorphism if, for every object and all morphisms , the following holds.

bimorphism

A morphism is called a bimorphism if it is both a monomorphism and an epimorphism.

section

A morphism is called a section if there exists a morphism such that .

retraction

A morphism is called a retraction if there exists a morphism such that .

isomorphism

A morphism is called an isomorphism if there exists a morphism such that and .