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 9: Categories,
of Proposition 9.6.2.1.2.
- Representably Full Morphisms in $\textbf{Rel}$. The representably full morphisms in $\textbf{Rel}$ are characterised in Chapter 6: Relations, Item 2 of Proposition 6.3.8.1.1.
