  This paper examines the category $\mathbf{Mat}_{\bullet}$ of pointed matroids
and strong maps from the point of view of Hall algebras. We show that
$\mathbf{Mat}_{\bullet}$ has the structure of a finitary proto-exact category -
a non-additive generalization of exact category due to Dyckerhoff-Kapranov. We
define the algebraic K-theory $K_* (\mathbf{Mat}_{\bullet})$ of
$\mathbf{Mat}_{\bullet}$ via the Waldhausen construction, and show that it is
non-trivial, by exhibiting injections $$\pi^s_n (\mathbb{S}) \hookrightarrow
K_n (\mathbf{Mat}_{\bullet})$$ from the stable homotopy groups of spheres for
all $n$. Finally, we show that the Hall algebra of $\mathbf{Mat}_{\bullet}$ is
a Hopf algebra dual to Schmitt's matroid-minor Hopf algebra.
