Multiplicative vertex algebras and quantum loop algebras

We define a multiplicative version of vertex coalgebras and show that various equivariant K-theoretic constructions of Hall algebras (KHAs) also admit a compatible multiplicative vertex coalgebra structure. In particular, this is true of the preprojective KHA of Varagnolo–Vasserot, which is (conjecturally) isomorphic to certain quantum loop algebras.