Explore the intricacies of R-matrices for the category O associated with untwisted quantum loop algebras Uq(g) in this 35-minute conference talk. Delve into the innovative approach of defining a remarkable functor that connects the category O of Uq(g) to that of Uh(g), where h = 1/q. Discover how applying this functor to known R-matrices yields new ones with fascinating properties. Examine the notable factorization of these new R-matrices into "stable maps" and investigate their unique pole structure, which is countable and partially characterizable. Gain insights into this advanced topic in mathematical physics, presented as part of the Workshop on Integrable systems, exactly solvable models and algebras at the Centre de recherches mathématiques.