Monomorphism

Definition

Definition with symbols

Suppose ${\mathcal {C}}$ is a category, $A,B\in \operatorname {Ob} {\mathcal {C}}$, and $f\in {\mathcal {C}}(A,B)$. We say that $f$ is monic, or is a monomorphism, if for any object $C$ and any $g,h\in {\mathcal {C}}(C,A)$, we have:

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

In other words, the morphism is left-cancellative.

Relation with other properties

Stronger properties

• Isomorphism
• Section

Related properties

• Epimorphism