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, Volume 12, Issue 1, pp 67–71 | Cite as

Liftungen von Tripeln

  • Dietmar Wätjen


For triplesS andT in a categoryOl, J. Beck [1] has shown the equiva-lence of a distributive law 1:TS→ST with a lifting ofT into the category ofS-algebras. Now in this paper it is proved that such a di-⋆ributive law is also equivalent with a lifting of S into the T-Kleisli-category. Distributive laws of mixed type are also considered. Each of the distributive laws GT→TG and TG→GT (with T a triple and G a cotriple inOl) produces a pair of dual liftings.


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  1. [1]:
    Beck,J.: Distributive Laws. Lecture Notes in Mathematics 80, 119–140, Berlin-Heidelberg-New York: Springer 1969.Google Scholar
  2. [2]:
    Eilenberg,S.,Moore,J.C.: Adjoint Functors and Triples. Illinois J. Math.9, 381–398 (1965).Google Scholar
  3. [3]:
    Kleisli,H.: Every standard construction is induced by a pair of adjoint functors. Proc. Amer. math. Soc.16, 544–546 (1965).Google Scholar
  4. [4]:
    Maranda,J.-M.: On Fundamental Constructions and Adjoint Functors. Canadian math. Bull.9, 581–591 (1966).Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Dietmar Wätjen
    • 1
  1. 1.Institut für Angewandte MathematikTechnische Universität Braunschweig33 Braunschweig

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