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 $.


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