| Theorem: Let $\mathcal{C}$ be a category and let $f:x\to y$ be a morphism in $\mathcal{C}$. | |
| Then $f$ is a monomorphism in $\mathcal{C}$ if and only if there exists a category $\mathcal{D}$ and a faithful functor $I:\mathcal{C}\to\mathcal{D}$ such that $f$ is a section in $\mathcal{D}$. |