  Let $k$ be a field. We describe necessary and sufficient conditions for a
$k$-linear abelian category to be a noncommutative projective line, i.e. a
noncommutative $\mathbb{P}^{1}$-bundle over a pair of division rings over $k$.
As an application, we prove that $\mathbb{P}^{1}_{n}$, Piontkovski's $n$th
noncommutative projective line, is the noncommutative projectivization of an
$n$-dimensional vector space.
