  Pursuing the similarity between the Kontsevich--Soibelman construction of the
cohomological Hall algebra of BPS states and Lusztig's construction of
canonical bases for quantum enveloping algebras, and the similarity between the
inetgrality conjecture for motivic Donaldson--Thomas invariants and the PBW
theorem for quantum enveloping algebras, we build a coproduct on the
cohomological Hall algebra associated to a quiver with potential. We also prove
a cohomological dimensional reduction theorem, further linking a special class
of cohomological Hall algebras with Yangians, and explaining how to connect the
study of character varieties with the study of cohomological Hall algebras.
