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. In other words, $F$ is dominant if for every object $d\in D$, there is an object $c\in C$ together with morphisms $r\colon F(c)\to d$ and $s\colon d\to F(c)$ such that $s\circ r=\operatorname {id} _{d}$.