Let $k$ be any field and $G$ a semi-abelian variety over $k$, i.e., an algebraic group that fits into an exact sequence
$$ 1 \to T \to G \to A \to 1$$
of algebraic groups, where $T$ is an algebraic torus and $A$ is an abelian variety. I have heard somewhere that, given an algebraic group $G$, if $G$ is semi-abelian then it is so in a unique way, meaning that $T$, $A$ and even the maps in the short exact sequence are uniquely determined by $G$. But I have failed to find a reference for this in full generality (or counterexamples).