  We develop the theory of (op)fibrations of 2-multicategories and use it to
define abstract six-functor-formalisms. We also give axioms for Wirthm\"uller
and Grothendieck formalisms (where either $f^!=f^*$ or $f_!=f_*$) or
intermediate formalisms where we have e.g. a natural morphism $f_! \rightarrow
f_*$. Finally, it is shown that a fibered multiderivator (in particular, a
closed monoidal derivator) can be interpreted as a six-functor-formalism on
diagrams (small categories). This gives, among other things, a considerable
simplification of the axioms and of the proofs of basic properties, and
clarifies the relation between the internal and external monoidal products in a
(closed) monoidal derivator. Our main motivation is the development of a theory
of derivator versions of six-functor-formalisms.
