Ringel duality and derivatives of non-additive functors

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Abstract

We prove that Ringel duality in the category of strict polynomial functors can be interpreted as derived functors of non-additive functors (in the sense of Dold and Puppe). We give applications of this fact for both theories.

References (44)

  • M. Chałupnik

    Koszul duality and extensions of exponential functors

    Adv. Math.

    (2008)
  • A. Beilinson et al.

    Koszul duality patterns in representation theory

    J. Amer. Math. Soc.

    (1996)
  • A.K. Bousfield, Homogeneous functors and their derived functors,...
  • L. Breen et al.

    Derived functors of non-additive functors and homotopy theory

    Algebr. and Geom. Topology

    (2011)
  • E. Cline et al.

    Finite-dimensional algebras and highest weight categories

    J. Reine Angew. Math.

    (1988)
  • E. Cline et al.

    Rational and generic cohomology

    Invent. Math.

    (1977)
  • E. Curtis

    Some relations between homotopy and homology

    Ann. of Math. (2)

    (1965)
  • A. Dold

    Homology of symmetric products and other functors of complexes

    Ann. of Math. (2)

    (1958)
  • A. Dold et al.

    Non additive functors, their derived functors and the suspension isomorphism

    Proc Nat. Acad. Sci. USA

    (1958)
  • A. Dold et al.

    Homologie nicht-additiver Funktoren. Anwendungen. (German)

    Ann. Inst. Fourier Grenoble

    (1961)
  • S. Donkin

    On tilting modules for algebraic groups

    Math. Z.

    (1993)
  • S. Eilenberg et al.

    Saunders on the groups H(Π,n). II. Methods of computation

    Ann. of Math. (2)

    (1954)
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