Six-functor-formalisms and fibered multiderivators (Q1783967)

The main motivation of this paper is, as the author writes, the development of a theory of derivator versions of six-functors-formalisms. The two first sections of the paper are devoted to developing, from a new unified point of view, the theory of (op)-fibrations of 2-multicategories and then, to define abstract six-functor-formalisms. In the next two sections, it is explained how classical six-functor-formalisms can be encoded as certain 1-bifibrations of 2-multicategories over the so defined multicategory of correspondences or, even that of correspondences of diagrams. In Sections 5 and 6, the author explains the equivalence, in appropriate contexts, between the notion of certain 1-bifibrations of 2-multicategories and that of fibered multiderivator. Finally, the author gives axioms for Wirthmüller and Grothendieck formalisms or intermediate formalisms, and he shows that a fibered multiderivator can be interpreted as a six-functor-formalisms on diagrams.