Item 2 (014N) — The Clowder Project

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Style 1	`book`	Alegreya Sans	`tcbthm`
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Style 3	`book`	Arno*	`amsthm`
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*To be replaced with Linus Romer's Elemaints when it is released.

Interaction With Adjunctions. Let $\webleft (F,G\webright )\colon \mathcal{C}\mathbin {\rightleftarrows }\mathcal{D}$ be an adjunction.
1. If $F$ is dominant, then $G$ is faithful.
2. The following conditions are equivalent:
  1. The functor $G$ is full.
  2. The restriction
    \[ \left.G\right\vert _{\mathrm{Im}_{F}}\colon \mathrm{Im}\webleft (F\webright )\to \mathcal{C} \]
    
    of $G$ to $\mathrm{Im}\webleft (F\webright )$ is full.

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