"trivial" exact sequence

Question

Let $A=B=C=\{0\}$.

Is $A\stackrel{f}\to B\stackrel{g}\to C$ a splitting exact sequence?

We have $Im(f)=ker(g)$ and there is an $h:C\to B$ such that $g\circ h=id_C$ so it should yield a splitting exact sequence but it's so trivial I don't know whether this is true.

Answer 1

Any short exact sequence $0\to A\to B\to C\to 0$ is split whenever $A=\{0\}$ or $C=\{0\}$. The reason is that the definition applies.