Item 5 (011Z) — The Clowder Project

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*To be replaced with Linus Romer's Elemaints when it is released.

Interaction With Precomposition II. If, for each $\mathcal{X}\in \text{Obj}\webleft (\mathsf{Cats}\webright )$, the precomposition functor
\[ F^{*} \colon \mathsf{Fun}\webleft (\mathcal{D},\mathcal{X}\webright ) \to \mathsf{Fun}\webleft (\mathcal{C},\mathcal{X}\webright ) \]

is full, then $F$ can fail to be full.

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