Linear epimorphism

Let $𝑇 : 𝑈 \to 𝑉$ be a $𝕂$ -linear map. The following statements are equivalent: #m/thm/linalg

$𝑇$ is surjective;
$𝑇$ is epic in $𝖵 𝖾 𝖼 𝗍 𝕂$ ;
$𝑇$ is split epic in $𝖵 𝖾 𝖼 𝗍 𝕂$ (assuming AC)
$c o k e r 𝑇 = {0}$ .

Proof

See Module epimorphism

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