= Solution
A <representation of a quiver> assigns a $k$-vector space $X_i$ to each vertex $i\in Q_0$ and a <linear map> $f_\rho:X_{s(\rho)}\to X_{t(\rho)}$ to each arrow $\rho\in Q_1$. Here $s(\rho)$ and $t(\rho)$ are its source and target. A <quiver representation morphism> $\theta:X\to Y$ is a family of <linear maps> $\theta_i:X_i\to Y_i$ such that every arrow square commutes:
$$
\boxed{\theta_{t(\rho)}f_\rho=g_\rho\theta_{s(\rho)}\quad(\rho\in Q_1).}
$$
Composition and identities are defined vertex by vertex. A <quiver representation morphism> is an isomorphism precisely when every $\theta_i$ is invertible.
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