  Drinfeld defined a unitarized R-matrix for any quantum group U_q(g). This
gives a commutor for the category of U_q(g) representations, making it into a
coboundary category. Henriques and Kamnitzer defined another commutor which
also gives U_q(g) representations the structure of a coboundary category. We
show that a particular case of Henriques and Kamnitzer's construction agrees
with Drinfeld's commutor. We then describe the action of Drinfeld's commutor on
a tensor product of two crystal bases, and explain the relation to the crystal
commutor.
