Item 5 (012H) — The Clowder Project

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Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

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

Interaction With Postcomposition. The following conditions are equivalent:
1. The functor $F\colon \mathcal{C}\to \mathcal{D}$ is fully faithful.
2. For each $\mathcal{X}\in \text{Obj}\webleft (\mathsf{Cats}\webright )$, the postcomposition functor
  \[ F_{*} \colon \mathsf{Fun}\webleft (\mathcal{X},\mathcal{C}\webright ) \to \mathsf{Fun}\webleft (\mathcal{X},\mathcal{D}\webright ) \]
  
  is fully faithful.
3. The functor $F\colon \mathcal{C}\to \mathcal{D}$ is a representably fully faithful morphism in $\mathsf{Cats}_{\mathsf{2}}$ in the sense of Chapter 9: Types of Morphisms in Bicategories, Definition 9.1.3.1.1.

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