Item 4 (0120) — The Clowder Project

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

Interaction With Precomposition III. If $F$ is essentially surjective and full, then the precomposition functor
\[ F^{*} \colon \mathsf{Fun}\webleft (\mathcal{D},\mathcal{X}\webright ) \to \mathsf{Fun}\webleft (\mathcal{C},\mathcal{X}\webright ) \]

is full (and also faithful by Item 3 of Proposition 8.5.1.1.2).

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