Here are some examples of corepresentably faithful morphisms.
- Corepresentably Faithful Morphisms in $\mathsf{Cats}_{\mathsf{2}}$. The corepresentably faithful morphisms in $\mathsf{Cats}_{\mathsf{2}}$ are characterised in Chapter 8: Categories, Item 4 of Proposition 8.5.1.1.2.
- Corepresentably Faithful Morphisms in $\textbf{Rel}$. Every morphism of $\textbf{Rel}$ is corepresentably faithful; see Chapter 5: Relations, Item 1 of Proposition 5.3.10.1.1.