Item 3 (0139) — The Clowder Project

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

Interaction With Precomposition. The following conditions are equivalent:
1. 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 conservative.
2. The equivalent conditions of Item 4 of Proposition 8.5.1.1.2 are satisfied.

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