  In 2021, Kashiwara-Kim-Oh-Park constructed cluster algebra structures on the
Grothendieck rings of certain monoidal subcategories of the category of
finite-dimensional representations of a quantum loop algebra, generalizing
Hernandez-Leclerc's pioneering work from 2010. They stated the problem of
finding explicit quivers for the seeds they used. We provide a solution by
using Palu's generalized mutation rule applied to the cluster categories
associated with certain algebras of global dimension at most 2, for example
tensor products of path algebras of representation-finite quivers. Thus, our
method is based on (and contributes to) the bridge, provided by cluster
combinatorics, between the representation theory of quantum groups and that of
quivers with relations.
