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

Pengjie Jiao

Published 2018-04-12Version 1

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