  The Reshetikhin-Turaev invariant, Turaev's TQFT, and many related
constructions rely on the encoding of certain tangles (n-string links, or
ribbon n-handles) as n-forms on the coend of a ribbon category. We introduce
the monoidal category of Hopf diagrams, and describe a universal encoding of
ribbon string links as Hopf diagrams. This universal encoding is an injective
monoidal functor and admits a straightforward monoidal retraction. Any Hopf
diagram with n legs yields a n-form on the coend of a ribbon category in a
completely explicit way. Thus computing a quantum invariant of a 3-manifold
reduces to the purely formal computation of the associated Hopf diagram,
followed by the evaluation of this diagram in a given category (using in
particular the so-called Kirby elements).
