Here are some examples of corepresentably full morphisms.
- Corepresentably Full Morphisms in $\mathsf{Cats}_{\mathsf{2}}$. The corepresentably full morphisms in $\mathsf{Cats}_{\mathsf{2}}$ are characterised in Chapter 8: Categories, Item 5 of Proposition 8.5.2.1.2.
- Corepresentably Full Morphisms in $\textbf{Rel}$. The corepresentably full morphisms in $\textbf{Rel}$ are characterised in Chapter 5: Relations, Item 2 of Proposition 5.3.10.1.1.