Cotorsion pairs in categories of quiver representations

We study the category $\mathrm{R}\mathrm{e}\mathrm{p}(Q,\mathcal{M})$ 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 $(\mathrm{\Phi }(\mathcal{A}),\mathrm{R}\mathrm{e}\mathrm{p}(Q,\mathcal{B}))$ and $(\mathrm{R}\mathrm{e}\mathrm{p}(Q,\mathcal{A}),\mathrm{\Psi }(\mathcal{B}))$ in $\mathrm{R}\mathrm{e}\mathrm{p}(Q,\mathcal{M})$. 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}$}, $\mathrm{d}\mathrm{g}$,\widetilde{$\mathcal{B}$})$and$($\mathrm{d}\mathrm{g}$,\widetilde{$\mathcal{A}$}, \widetilde{$\mathcal{B}$})$ in the category $\mathrm{C}\mathrm{h}(\mathcal{M})$ of chain complexes in $\mathcal{M}$. Special cases of our results recover descriptions of the projective and injective objects in $\mathrm{R}\mathrm{e}\mathrm{p}(Q,\mathcal{M})$ proved by Enochs, Estrada, and Garcia Rozas.