For a Dynkin quiver $Q$ (i.e. Dynkin graph of a simple Lie algebra $\mathfrak{g}$ of type ADE with
an orientation), Hernandez-Leclerc defined a monoidal subcategory $\mathcal{C}_{Q}$ of the category
of finite-dimensional modules over the quantum loop algebra associated with $\mathfrak{g}$. They
proved that its Grothendiek ring is isomorphic to the coordinate algebra of the maximal unipotent
subgroup associated with $\mathfrak{g}$ and that the classes of simple modules correspond to the
dual canonical basis elements. In this talk, we see that a "central completion" of the category
$\mathcal{C}_{Q}$ has a structure of affine highest weight category. We rely on Nakajima's
geometric method using the equivariant K-theory of graded quiver varieties. As an application, we
conclude that Kang-Kashiwara-Kim's generalized quantum affine Schur-Weyl duality functor gives a
monoidal equivalence between the Hernandez-Leclerc category $\mathcal{C}_{Q]$ and the category of
finite-dimensional modules over the quiver Hecke (KLR) algebra associated with $Q$, assuming the
simpleness of poles of normalized R-matrices for type E.