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

Multiplicative vertex algebras and quantum loop algebras