  We develop vertex and factorisation algebra analogues of the theory of
quasitriangular bialgebras. Analogously to the classical theory, we prove their
categories of representations are controlled by spectral R-matrices. In the
vertex algebra case this generalises previous notions due to Etingof-Kazhdan
and Frenkel-Reshetikhin. Finally we give examples, including Borcherds twists
and homology vertex algebras.
