A function \(f\colon X\to Y\) is surjective if and only if it has a right inverse, i.e. there is a function \(g:Y\to X\) such that \(f\circ g=\id_Y\).
A function \(f\colon X\to Y\) is surjective if and only if it has a right inverse, i.e. there is a function \(g:Y\to X\) such that \(f\circ g=\id_Y\).