Morphism

Epimorphism

A epimorphism is a right-cancellable morphism (denoted with ). A morphism is epic iff for any and 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.

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