Here are some examples of representably faithful morphisms.
- Representably Faithful Morphisms in $\mathsf{Cats}_{\mathsf{2}}$. The representably faithful morphisms in $\mathsf{Cats}_{\mathsf{2}}$ are precisely the faithful functors; see Chapter 8: Categories, Item 1 of Proposition 8.5.1.1.2.
- Representably Faithful Morphisms in $\textbf{Rel}$. Every morphism of $\textbf{Rel}$ is representably faithful; see Chapter 5: Relations, Item 1 of Proposition 5.3.8.1.1.