Projective objects in the category of pointwise finite dimensional representations of an interval finite quiver

For an interval finite quiver $Q$, we introduce a class of flat representations. We classify the indecomposable projective objects in the category $\mathrm{r}\mathrm{e}\mathrm{p}(Q)$ of pointwise finite dimensional representations. We show that an object in $\mathrm{r}\mathrm{e}\mathrm{p}(Q)$ is projective if and only if it is a direct sum of countably generated flat representations.