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

    given by postcomposition by $f$ is fully faithful.


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