Quiver moduli and quantum loop algebras

A classic result of Hernandez-Leclerc and Kashiwara-Kim-Oh-Park relates the q-characters of so-called reachable simple modules of quantum affine algebras to the Euler characteristics of certain quiver moduli spaces. We categorify and generalize this relation to all simple modules in the Hernandez-Jimbo category O using critical K-theory (our results hold for quantum toroidal as well as quantum affine algebras)