Epimorphism

Split epimorphism

A split epimorphism is a morphism with a preïnverse or section , #m/def/cat so that . Note that is necessarily an epimorphism, and has the dual property of being a Split monomorphism. Furthermore need not be unique.

Properties

Let be a split epimorphism with section

1. is the coëqualizer of and , hence it is regularly epic.

See dual Properties.

See also

• Split extension
• External Axiom of Choice

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