• For each $X\in \text{Obj}\webleft (\mathsf{Cats}\webright )$, the postcomposition functor
    \[ F_{*}\colon \mathsf{Fun}\webleft (\mathcal{X},\mathcal{C}\webright )\to \mathsf{Fun}\webleft (\mathcal{X},\mathcal{D}\webright ) \]

    is an equivalence of categories.


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