Hall algebras and quantum symmetric pairs of Kac-Moody type II

We extend the $\mathrm{ı}$Hall algebra realization of $\mathrm{ı}$quantum groups arising from quantum symmetric pairs, which establishes an injective homomorphism from the universal $\mathrm{ı}$quantum group of Kac-Moody type to the $\mathrm{ı}$Hall algebra associated to an arbitrary $\mathrm{ı}$quiver (not necessarily virtually acyclic). This generalizes Lu-Wang’s result.