Monomorphism

Definition

Definition with symbols

Suppose $\mathcal{C}$ is a category, $A,B\in \mathrm{O}\mathrm{b}\mathcal{C}$, 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:

$f\circ g=f\circ h⟹g=h$.

In other words, the morphism is left-cancellative.

Relation with other properties

Stronger properties

• Isomorphism
• Section

Related properties

• Epimorphism