Here are some examples of strict epimorphisms.
- Strict Epimorphisms in $\mathsf{Cats}_{\mathsf{2}}$. The strict epimorphisms in $\mathsf{Cats}_{\mathsf{2}}$ are characterised in Chapter 8: Categories, Item 1 of Proposition 8.6.3.1.2.
- Strict Epimorphisms in $\textbf{Rel}$. The strict epimorphisms in $\textbf{Rel}$ are characterised in Chapter 5: Relations, Proposition 5.3.9.1.1.