Dominant functor

In category theory, an abstract branch of mathematics, a dominant functor is a functor F : C → D in which every object of D is a retract of an object of the form F(x) for some object X of C.^[1] In other words, $F$ is dominant if for every object $d \in D$ , there is an object $c \in C$ together with morphisms $r : F (c) \to d$ and $s : d \to F (c)$ such that $s \circ r = {id}_{d}$ .