The Clowder Project

Here are some examples of corepresentably fully faithful morphisms.

1. Corepresentably Fully Faithful Morphisms in $\mathsf{Cats}_{\mathsf{2}}$. The fully faithful epimorphisms in $\mathsf{Cats}_{\mathsf{2}}$ are characterised in Chapter 8: Categories, Item 9 of Proposition 8.5.3.1.2.
2. Corepresentably Fully Faithful Morphisms in $\textbf{Rel}$. The corepresentably fully faithful morphisms of $\textbf{Rel}$ coincide (Chapter 5: Relations, Item 3 of Proposition 5.3.10.1.1) with the corepresentably full morphisms in $\textbf{Rel}$, which are characterised in Chapter 5: Relations, Item 2 of Proposition 5.3.10.1.1.