Here are some examples of representably full morphisms.
- Representably Full Morphisms in $\mathsf{Cats}_{\mathsf{2}}$. The representably full morphisms in $\mathsf{Cats}_{\mathsf{2}}$ are precisely the full functors; see Chapter 8: Categories, Item 1 of Proposition 8.5.2.1.2.
- Representably Full Morphisms in $\textbf{Rel}$. The representably full morphisms in $\textbf{Rel}$ are characterised in Chapter 5: Relations, Item 2 of Proposition 5.3.8.1.1.