Morphism

Epimorphism

A epimorphism is a right-cancellable morphism (denoted with ). A morphism is epic iff for any and #m/def/cat

In a function is a epic iff it is surjective iff (assuming the Axiom of Choice) it is right-invertible (i.e. split epic), but these are not equivalent in every concrete category, rather:

graph LR;
  right-invertible ==>|implies| surjective ==>|implies| epic

Properties

See the dual properties.

  1. If is epic then is epic.
Proof of 1

Dualize the corresponding proofs for properties of monomorphisms.

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