  We approach the classification of Lie bialgebra structures on simple Lie
algebras from the viewpoint of descent and non-abelian cohomology. We achieve a
description of the problem in terms faithfully flat cohomology over an
arbitrary ring over $\mathbb{Q}$, and solve it for Drinfeld-Jimbo Lie
bialgebras over fields of characteristic zero. We consider the classification
up to isomorphism, as opposed to equivalence, and treat split and non-split Lie
algebras alike. We moreover give a new interpretation of scalar multiples of
Lie bialgebras hitherto studied using twisted Belavin-Drinfeld cohomology.
