  We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories,
focusing on the generators for their quantized coordinate rings. We show that
there is a surjective map from a shifted Yangian onto the quantized Coulomb
branch, once the deformation parameter is set to $\hbar =1$. In finite ADE
type, this extends to a surjection over $\mathbb{C}[\hbar]$. We also show that
these algebras are generated by the dressed minuscule monopole operators, for
an arbitrary quiver (this is similar to the proof of Theorem 4.29 in
arXiv:1811.12137). Finally, we describe how the KLR Yangian algebra from
arXiv:1806.07519 is related to Webster's extended BFN category. This paper
provides proofs for two results which were announced in arXiv:1806.07519.
