Abstract
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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Literatur
Beck,J.: Distributive Laws. Lecture Notes in Mathematics 80, 119–140, Berlin-Heidelberg-New York: Springer 1969.
Eilenberg,S.,Moore,J.C.: Adjoint Functors and Triples. Illinois J. Math.9, 381–398 (1965).
Kleisli,H.: Every standard construction is induced by a pair of adjoint functors. Proc. Amer. math. Soc.16, 544–546 (1965).
Maranda,J.-M.: On Fundamental Constructions and Adjoint Functors. Canadian math. Bull.9, 581–591 (1966).
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Wätjen, D. Liftungen von Tripeln. Manuscripta Math 12, 67–71 (1974). https://doi.org/10.1007/BF01166234
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DOI: https://doi.org/10.1007/BF01166234