Counting absolutely indecomposable objects in categories of quiver representations and vector bundle

I will talk about the work https://arxiv.org/abs/1612.01733, which is devoted to counting absolutely indecomposable objects in certain categories, the main examples of which are provided by quiver representations and vector bundles with a parabolic structure on a projective curve. More precisely, the result applies to k-linear (where k is a finite field) Karoubian categories C, such that C is equipped with a k-linear functor to finite-dimensional graded vector spaces and the objects of C can be identified with k-points of a smooth Artin stack.