In detail, a functor $F\colon \mathcal{C}\to \mathcal{D}$ is representably faithful on cores if, given a diagram of the form
if $\alpha $ and $\beta $ are natural isomorphisms and we have
\[ \text{id}_{F}\mathbin {\star }\alpha =\text{id}_{F}\mathbin {\star }\beta , \]
then $\alpha =\beta $.