The Clowder Project

Here are some examples of corepresentably faithful morphisms.

1. Corepresentably Faithful Morphisms in $\mathsf{Cats}_{\mathsf{2}}$. The corepresentably faithful morphisms in $\mathsf{Cats}_{\mathsf{2}}$ are characterised in Chapter 9: Categories, Item 5 of Proposition 9.6.1.1.2.
2. Corepresentably Faithful Morphisms in $\textbf{Rel}$. Every morphism of $\textbf{Rel}$ is corepresentably faithful; see Chapter 6: Relations, Item 1 of Proposition 6.3.10.1.1.