  We define and study the category $\RepQ$ of representations of a quiver in
$\VFun$ - the category of vector spaces "over $\Fun$". $\RepQ$ is an
$\Fun$-linear category possessing kernels, co-kernels, and direct sums.
Moreover, $\RepQ$ satisfies analogues of the Jordan-H\"older and Krull-Schmidt
theorems. We are thus able to define the Hall algebra $\HQ$ of $\RepQ$, which
behaves in some ways like the specialization at $q=1$ of the Hall algebra of
$\on{Rep}(\Q, \mathbf{F}_q)$. We prove the existence of a Hopf algebra
homomorphism of $ \rho': \U(\n_+) \rightarrow \HQ$, from the enveloping algebra
of the nilpotent part $\n_+$ of the Kac-Moody algebra with Dynkin diagram
$\bar{\Q}$ - the underlying unoriented graph of $\Q$. We study $\rho'$ when
$\Q$ is the Jordan quiver, a quiver of type $A$, the cyclic quiver, and a tree
respectively.
