  We identify the trace, or 0th Hochschild homology, of type ADE categorified
quantum groups with the corresponding current algebra of the same type. To
prove this, we show that 2-representations defined using categories of modules
over cyclotomic (or deformed cyclotomic) quotients of KLR-algebras correspond
to local (or global) Weyl modules. We also investigate the implications for
centers of categories in 2-representations of categorified quantum groups.
