Quantum version of Deligne's conjecture for the exceptional series

Let $\mathsf{QExc}_{R,v,w}$ be the quantum exceptional diagram category. A trivalent ribbon category is a ribbon category generated by a trivalent vertex, and a ribbon functor preserves the ribbon structure. Quantum Deligne conjecture. There exist a ring $R$ satisfying the defining hypotheses of the quantum exceptional category, a trivalent ribbon category $\mathsf{QExc}^{Del}_{R,v,w}$ with non-negative integers as objects and finitely generated $R$-modules as morphism spaces, and a ribbon functor $\operatorname{Qeval}:\mathsf{QExc}_{R,v,w}\to\mathsf{QExc}^{Del}_{R,v,w}$ that is the identity on objects, surjective on morphisms, and sends the trivalent vertex to the trivalent vertex. This is the proposed quantum categorical realization of the exceptional series and is presented as a partial quantum counterpart of the classical Deligne conjecture; the supplied statement does not include further generic semisimplicity or specialization properties.