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