Item 7 (011Q) — 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.

The functor $F$ is dominant (Definition 9.7.1.1.1), i.e. every object of $\mathcal{D}$ is a retract of some object in $\mathrm{Im}\webleft (F\webright )$:
- For each $B\in \text{Obj}\webleft (\mathcal{D}\webright )$, there exist:
  - An object $A$ of $\mathcal{C}$;
  - A morphism $s\colon B\to F\webleft (A\webright )$ of $\mathcal{D}$;
  - A morphism $r\colon F\webleft (A\webright )\to B$ of $\mathcal{D}$;
  such that $r\circ s=\text{id}_{B}$.

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