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