Epimorphism

A epimorphism is a right-cancellable morphism (denoted with $↠$ ). A morphism $𝑒 : 𝑋 \to 𝑌$ is epic iff for any $𝑍 \in 𝖢$ and $𝑓, 𝑔 : 𝑌 \to 𝑍$ #m/def/cat

𝑓 \circ 𝑒 = 𝑔 \circ 𝑒 ⟹ 𝑓 = 𝑔

In $𝖲 𝖾 𝗍$ 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.

If $𝑓 𝑔$ is epic then $𝑓$ is epic.

Proof of 1

Dualize the corresponding proofs for properties of monomorphisms.

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