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.{{citation|journal=Applied Categorical Structures|date=March 2014|title=On normal tensor functors and coset decompositions for fusion categories|first1=A.|last1=Bruguières|first2=Sebastian|last2=Burciu|doi=10.1007/s10485-014-9371-x|arxiv=1210.3922}}. In other words, $F$ is dominant if for every object $d\; \backslash in\; D$, there is an object $c\; \backslash in\; C$ together with morphisms $r\backslash colon\; F(c)\; \backslash to\; d$ and $s\backslash colon\; d\; \backslash to\; F(c)$ such that $s\; \backslash circ\; r=\backslash operatorname\{id\}\_\{d\}$.