Six-functor-formalisms and fibered multiderivators

• Fritz Hörmann ^[1]
  1. [1] Universität Freiburg, Freiburg, Germany
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 4, 2018, págs. 2841-2925
• Idioma: inglés
• DOI: 10.1007/s00029-018-0424-0
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• Resumen

  • We develop the theory of (op)fibrations of 2-multicategories and use it to define abstract six-functor-formalisms. We also give axioms for Wirthmüller and Grothendieck formalisms (where either f ! = f ∗ or f! = f∗) or intermediate formalisms where we have e.g. a natural morphism f! → 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.