2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158827We study the unitarizability of premodular categories constructed from representations of quantum group at roots of unity. We introduce \emph{Grothendieck unitarizability} as a natural generalization of unitarizability to any class of premodular categories with a common Grothendieck semiring. We obtain new results for quantum groups of Lie types $F_4$ and $G_2$, and improve the known results for Lie types $B$ and $C$.Version 2: proof of conjecture provided by referee, now Theorem 3.8 is sharp. To appear in J. Pure Appl. AlgebraQuantum Algebra17B37 (Primary); 18D10, 20G42 (Secondary)text