The Clowder Project

Here are some examples of representably faithful morphisms.

1. Representably Faithful Morphisms in $\mathsf{Cats}_{\mathsf{2}}$. The representably faithful morphisms in $\mathsf{Cats}_{\mathsf{2}}$ are precisely the faithful functors; see Chapter 9: Preorders, Item 2 of Proposition 9.6.1.1.2.
2. Representably Faithful Morphisms in $\textbf{Rel}$. Every morphism of $\textbf{Rel}$ is representably faithful; see Chapter 6: Relations, Item 1 of Proposition 6.3.8.1.1.