Quiver matroids are defined with morphisms and bundles; their F1-moduli spaces have point counts equaling the Euler characteristic of complex quiver Grassmannians in nice cases.
Matroid theory , volume 21 of Oxford Graduate Texts in Mathematics
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Quiver matroids -- Matroid morphisms, quiver Grassmannians, their Euler characteristics and $\mathbb{F}_1$-points
Quiver matroids are defined with morphisms and bundles; their F1-moduli spaces have point counts equaling the Euler characteristic of complex quiver Grassmannians in nice cases.