universal split epimorphism

This is the morphism $p : 1 \to 0$ in the walking splitting, see there for details. It can also be seen as the unique morphism $\IF_2 \to 0$ in the category of $\IF_2$-vector spaces of dimension $\leq 1$. It provides a basic example of a split epimorphism (and hence regular and strict epimorphism) which is not effective.