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

Abstract

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 pointwise finite dimensional representations. We show that an object in $\mathrm{rep}(Q)$ is projective if and only if it is a direct sum of countably generated flat representations.

arXiv comment20 pages, final version

References in corpus (2)

• Infinite-dimensional vector bundles in algebraic geometry (an introduction)
• Decompositions of locally finite endo-length modules over a skeletally small category

Cited by in corpus (1)

• The generalized Auslander-Reiten duality on a module category