Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Six Functor Formalisms and Fibered Multiderivators   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.

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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con