Then $f$ is an invertible map if and only if there exists a D18: Map $g : Y \to X$ such that
| (1) | \begin{equation} \forall \, x \in X : g(f(x)) = x \end{equation} | (D977: Left-invertible map) |
| (2) | \begin{equation} \forall \, y \in Y : f(g(y)) = x \end{equation} | (D978: Right-invertible map) |