Exercise 9.2.7.8. Let $f: A \twoheadrightarrow B$ be a surjective function between sets, and let $g: X \hookrightarrow Y$ be an injective function between sets. Show that:
The morphism $f$ is left orthogonal to $g$ (in the category of sets).
The morphism $g$ is weakly left orthogonal to $f$.
Unless either $f$ or $g$ is a bijection, the morphism $g$ is not left orthogonal to $f$.