  We study the category $\mathrm{Rep}(Q,\mathcal{M})$ of representations of a
quiver $Q$ with values in an abelian category $\mathcal{M}$. Under certain
assumptions, we show that every cotorsion pair $(\mathcal{A},\mathcal{B})$ in
$\mathcal{M}$ induces two (explicitly described) cotorsion pairs
$(\Phi(\mathcal{A}),\mathrm{Rep}(Q,\mathcal{B}))$ and
$(\mathrm{Rep}(Q,\mathcal{A}),\Psi(\mathcal{B}))$ in
$\mathrm{Rep}(Q,\mathcal{M})$. This is akin to a result by Gillespie, which
asserts that a cotorsion pair $(\mathcal{A},\mathcal{B})$ in $\mathcal{M}$
induces cotorsion pairs $(\widetilde{\mathcal{A}},
\mathrm{dg}\,\widetilde{\mathcal{B}})$ and
$(\mathrm{dg}\,\widetilde{\mathcal{A}}, \widetilde{\mathcal{B}})$ in the
category $\mathrm{Ch}(\mathcal{M})$ of chain complexes in $\mathcal{M}$.
Special cases of our results recover descriptions of the projective and
injective objects in $\mathrm{Rep}(Q,\mathcal{M})$ proved by Enochs, Estrada,
and Garcia Rozas.
