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

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