• For each $X\in \text{Obj}\webleft (\mathcal{C}\webright )$, the functor
    \[ f^{*}\colon \mathsf{Core}\webleft (\mathsf{Hom}_{\mathcal{C}}\webleft (B,X\webright )\webright )\to \mathsf{Core}\webleft (\mathsf{Hom}_{\mathcal{C}}\webleft (A,X\webright )\webright ) \]

    given by precomposition by $f$ is fully faithful.


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