Linear map

Linear epimorphism

Let 𝑇 :𝑈 →𝑉 be a 𝕂-linear map. The following statements are equivalent: linalg

• 𝑇 is surjective;
• 𝑇 is epic in Category of vector spaces;
• 𝑇 is split epic in Category of vector spaces (assuming AC)
• coker⁡𝑇 ={0}.

Proof

See Module epimorphism

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