Epimorphism

Definition

Suppose ${\mathcal {C}}$ is a category, $A,B\in \operatorname {Ob} {\mathcal {C}}$, and $f\in {\mathcal {C}}(A,B)$. $f$ is termed an epimorphism, or epic, if for any object $C$ and any $g,h\in {\mathcal {C}}(B,C)$ we have:

$g\circ f=h\circ f\implies g=h$.

Relation with other properties

Stronger properties

• Isomorphism
• Retraction

Related properties

• Monomorphism